Physics: Refraction and Reflection Concepts

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Questions and Answers

An index of refraction less than one for a medium implies which of the following?

  • The speed of light in the medium is less than in vacuum.
  • The speed of light in the medium is the same as in vacuum.
  • The speed of light in the medium is greater than in vacuum. (correct)
  • Refraction is not possible.

What happens to the speed of light when it enters a material with a higher index of refraction?

  • It decreases. (correct)
  • It stays the same.
  • It increases.
  • It first increases then decreases.

Another name for the POLARIZING ANGLE is which of the following?

  • Brewster angle (correct)
  • Land angle
  • Moles angle
  • Refracted angle

Spherical lenses are affected by which aberration?

<p>Both spherical and chromatic aberration. (D)</p> Signup and view all the answers

If a person's face is 30 cm in front of a concave mirror and the image is erect and 1.5 times larger, what is the focal length of the mirror?

<p>50 cm (D)</p> Signup and view all the answers

When comparing two diffraction gratings that differ only in the number of slits, which statement is correct?

<p>The orders are better defined with the 4-slit grating. (B)</p> Signup and view all the answers

Which material has the slowest speed of light?

<p>Diamond (A)</p> Signup and view all the answers

The warning 'OBJECTS IN MIRROR ARE CLOSER THAN THEY APPEAR' indicates that the mirror is which type?

<p>Convex (C)</p> Signup and view all the answers

What type of images do concave lenses primarily produce?

<p>Always virtual (B)</p> Signup and view all the answers

What phenomenon is crucial for fiber optics to function?

<p>Total internal reflection (B)</p> Signup and view all the answers

What causes the colors observed on an oil slick?

<p>Interference (A)</p> Signup and view all the answers

If you stand at the center of curvature of a concave mirror, how will your image appear?

<p>Same size and inverted (D)</p> Signup and view all the answers

What happens to light when it travels from crown glass into water?

<p>It refracts and reflects (A)</p> Signup and view all the answers

What is chromatic aberration mainly caused by?

<p>Dispersion (A)</p> Signup and view all the answers

What must the incident angle be for total internal reflection to occur?

<p>Greater than the critical angle (A)</p> Signup and view all the answers

What is the result of light traveling from a denser medium to a less dense medium at the critical angle?

<p>Total internal reflection occurs (D)</p> Signup and view all the answers

How does the index of refraction of diamond affect the speed of light traveling through it?

<p>Light travels slower in diamond than in vacuum (B)</p> Signup and view all the answers

At the first maxima of a double-slit experiment, how does light from each opening arrive?

<p>In phase (A)</p> Signup and view all the answers

What is the index of refraction inside a certain transparent material if the critical angle is found to be 48°?

<p>1.48 (A)</p> Signup and view all the answers

What is the angular separation between the refracted red and refracted blue beams in glass, given their respective indices of refraction?

<p>0.341° (B)</p> Signup and view all the answers

If you stand in front of a convex mirror at a distance equal to its radius of curvature, what will you observe?

<p>You will see your image and you will appear smaller. (C)</p> Signup and view all the answers

What is the intensity of the beam after passing through two polarizers with the second polarizer rotated 40° to the first?

<p>0.41 (B)</p> Signup and view all the answers

When light passes through a prism, which color is refracted the most?

<p>violet (C)</p> Signup and view all the answers

The direction of polarization for a beam of light is defined as what?

<p>the direction of the electric field's vibration. (A)</p> Signup and view all the answers

What is the focal length of a double convex lens made of glass with an index of refraction of 1.60 and radii of curvature of 46 cm?

<p>36 cm (C)</p> Signup and view all the answers

As a soap film becomes much thinner than the wavelength of blue light, how does it appear?

<p>It appears blue since all other colors are transmitted. (C)</p> Signup and view all the answers

Which diffraction grating produces greater dispersion: one with 4000 lines per cm or one with 6000 lines per cm?

<p>The 6000-line grating produces the greater dispersion. (C)</p> Signup and view all the answers

What happens to the distance between adjacent maxima when the slit separation in a double-slit experiment is cut in half?

<p>It increases to 2 cm. (D)</p> Signup and view all the answers

What will the angle of refraction be when light enters air from water?

<p>Less than the angle of incidence. (D)</p> Signup and view all the answers

As the frequency of light increases in common transparent media, what happens to the index of refraction?

<p>It increases. (B)</p> Signup and view all the answers

What type of lens has a power of +10 Diopters and a first surface center of curvature in front of the lens?

<p>double convex (A)</p> Signup and view all the answers

Liquid Crystal Displays (LCDs) depend upon which principle for their operation?

<p>polarization (D)</p> Signup and view all the answers

What is the angle of refraction in glass if the incident angle is 45°?

<p>Less than 45° (C)</p> Signup and view all the answers

What orientation is the image of a rare stamp viewed through a magnifying glass when the stamp is close to the glass?

<p>Either the same orientation or upside-down (D)</p> Signup and view all the answers

When a red and blue light beam passes through a glass plate, how do the separate beams emerge?

<p>Parallel, with the blue beam below the red (D)</p> Signup and view all the answers

What type of image is formed by a converging lens when the object is inside the focal point?

<p>Virtual (C)</p> Signup and view all the answers

What happens to light rays with an angle of incidence greater than the critical angle of 48.8° when passing from water into air?

<p>Totally reflected (C)</p> Signup and view all the answers

For destructive interference, the path difference is given by which values of m?

<p>1, 3, 5, 7,... (B)</p> Signup and view all the answers

The condition for X-ray diffraction maxima is attributed to which scientist?

<p>Bragg (A)</p> Signup and view all the answers

If the index of refraction of a medium is 1.5, what is the speed of light in that medium?

<p>2.0 × 10^8 m/s (B)</p> Signup and view all the answers

What is the expected pattern on the screen after light passes through two narrow parallel slits?

<p>A series of alternating light and dark bands (C)</p> Signup and view all the answers

What is the distance between two slits if the third bright fringe is at an angle of 7.0° for a wavelength of 490 nm?

<p>3.6 × 10^-5 m (B)</p> Signup and view all the answers

When light rays are in phase, which statement is true?

<p>Electric fields of both rays reach their maxima simultaneously. (D)</p> Signup and view all the answers

What changes when light enters a medium of different optical density?

<p>Only speed and wavelength change (D)</p> Signup and view all the answers

How far must an object be placed in front of a lens with a focal length of 50.0 mm to form a virtual image magnified by a factor of three?

<p>33.3 mm (B)</p> Signup and view all the answers

At what angle will the second order line appear for an X-ray beam making an angle of 20°?

<p>40° (D)</p> Signup and view all the answers

What happens to light traveling at an angle into a denser medium?

<p>It is refracted toward the normal (C)</p> Signup and view all the answers

What does an index of refraction less than one indicate about the speed of light in that medium?

<p>The speed of light in the medium is greater than in vacuum. (D)</p> Signup and view all the answers

When light passes into a medium with a higher index of refraction, its speed changes in what way?

<p>The speed decreases. (D)</p> Signup and view all the answers

What is another name for the angle at which light is completely polarized upon reflection?

<p>Brewster angle (D)</p> Signup and view all the answers

What type of aberration do spherical lenses experience?

<p>Both spherical and chromatic aberration. (B)</p> Signup and view all the answers

Given a concave shaving mirror where a person's face is 30 cm away and the image is 1.5 times larger, what is the focal length of the mirror?

<p>20 cm (B)</p> Signup and view all the answers

If two diffraction gratings with the same slit separation have different numbers of slits, what can be said about the light patterns they produce?

<p>The grating with more slits produces a pattern with greater order separation. (D)</p> Signup and view all the answers

Which of the following materials has the slowest speed of light?

<p>Diamond (D)</p> Signup and view all the answers

What type of mirror is indicated if a rear-view mirror states 'OBJECTS IN MIRROR ARE CLOSER THAN THEY APPEAR'?

<p>Convex mirror (D)</p> Signup and view all the answers

Which type of image is always formed by a concave lens?

<p>Always virtual (C)</p> Signup and view all the answers

What phenomenon allows fiber optics to function effectively?

<p>Total internal reflection (B)</p> Signup and view all the answers

What causes the vivid colors observed on an oil slick?

<p>Interference (A)</p> Signup and view all the answers

If you stand exactly at the center of curvature of a concave mirror, how will your image appear?

<p>Inverted and the same size (D)</p> Signup and view all the answers

What occurs when light is incident at the critical angle while traveling from crown glass to water?

<p>Total internal reflection (B)</p> Signup and view all the answers

What type of aberration is primarily caused by the variation of the refractive index with wavelength?

<p>Chromatic aberration (B)</p> Signup and view all the answers

How does sunlight create a rainbow in the atmosphere?

<p>By dispersion, refraction, and reflection (D)</p> Signup and view all the answers

What results when light reflects off a glass surface from air?

<p>A 180° phase change occurs (D)</p> Signup and view all the answers

Which is true about the order of light interference patterns in a double-slit experiment at the first maxima?

<p>The light waves arrive completely in phase (B)</p> Signup and view all the answers

What can be concluded when light travels from one medium to another and the index of refraction is higher in the first medium?

<p>Light slows down (C)</p> Signup and view all the answers

What happens to the light rays with an angle of incidence greater than the critical angle when passing from water into air?

<p>They are totally reflected. (D)</p> Signup and view all the answers

In a two-slit experiment, what pattern will be observed on the screen when monochromatic light passes through two narrow parallel slits?

<p>A series of alternating bright and dark fringes. (A)</p> Signup and view all the answers

What is the image formed when an object is inside the focal point of a converging lens?

<p>Virtual and upright. (A)</p> Signup and view all the answers

If a light beam composed of red and blue light emerges from glass, how are the beams oriented?

<p>Non-parallel, blue below red. (B)</p> Signup and view all the answers

How far from a lens of focal length 50.0 mm must the object be placed to form a virtual image that is magnified by a factor of three?

<p>33.3 mm. (A)</p> Signup and view all the answers

What defines two light rays being 'in phase' with each other?

<p>Their electric fields reach maxima simultaneously. (A)</p> Signup and view all the answers

For destructive interference in wave patterns, what values of m are used in the path difference formula?

<p>m = 1, 3, 5,... (C)</p> Signup and view all the answers

When light travels from a less dense medium to a denser medium at an incident angle greater than the critical angle, what occurs?

<p>It is reflected. (B)</p> Signup and view all the answers

What happens to the speed of light as it travels from air into glass?

<p>It slows down. (D)</p> Signup and view all the answers

What is the angle of refraction when light exits a 45° glass prism into the air?

<p>45°. (D)</p> Signup and view all the answers

When two parallel rays reflect off a concave mirror, where do they intersect?

<p>At the focal point. (A)</p> Signup and view all the answers

What type of aberration do spherical mirrors experience?

<p>Both chromatic and spherical aberration. (D)</p> Signup and view all the answers

What is the angular separation between the refracted red and refracted blue beams while in the glass?

<p>0.341° (B)</p> Signup and view all the answers

If you stand in front of a convex mirror at a distance equal to its radius of curvature, how will the image appear?

<p>You will see your image smaller. (B)</p> Signup and view all the answers

What is the intensity of light after passing through two polarizers, with the second rotated 40° to the first, if the initial intensity is 1?

<p>0.64 (D)</p> Signup and view all the answers

Which color is refracted the most when light passes through a prism?

<p>Violet (B)</p> Signup and view all the answers

What defines the direction of polarization for a beam of light?

<p>The direction of the electric field's vibration. (B)</p> Signup and view all the answers

Which diffraction grating produces the greater dispersion?

<p>The 6000 lines/cm grating produces greater dispersion. (B)</p> Signup and view all the answers

What happens to the distance between adjacent maxima when the slit separation in a double-slit experiment is halved?

<p>It increases to 2 cm. (A)</p> Signup and view all the answers

What will be the angle of refraction when light enters air from water?

<p>Less than the angle of incidence. (A)</p> Signup and view all the answers

What kind of lens produces a power of +10 Diopters and has a first surface center of curvature in front of the lens?

<p>Double convex (D)</p> Signup and view all the answers

What principle does a Liquid Crystal Display (LCD) depend upon for its operation?

<p>Polarization (C)</p> Signup and view all the answers

If you look at the bottom side of a shiny spoon, what image will you see?

<p>A little you, upside down. (D)</p> Signup and view all the answers

Flashcards

Index of Refraction < 1

The index of refraction (n) is a measure of how much light bends when it enters a medium. If the index of refraction is less than 1, it implies that the speed of light is greater in the medium than in a vacuum.

Refraction in Higher Index Medium

When light enters a medium with a higher index of refraction (n), it slows down. The higher the index, the more the light bends.

Polarizing Angle

The polarizing angle, also known as Brewster's angle, is the angle at which unpolarized light incident on a surface becomes completely polarized.

Spherical Aberration

Spherical aberration is a type of optical distortion that occurs in spherical lenses. It happens when light rays passing through different parts of the lens focus at slightly different points, causing a blurry image.

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Concave Mirror: Erect Image

When an object is placed within the focal length of a concave mirror, the image formed is virtual, upright, and magnified.

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Diffraction Grating: Slit Separation

The separation between orders (brightness maxima) in a diffraction grating pattern depends on the slit spacing (d) and the wavelength of light (λ). Increasing the number of slits does not change the spacing between orders but improves sharpness.

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Speed of Light in Materials

The speed of light is slowest in a material with the highest refractive index. The order of materials from fastest to slowest for light is: air, water, oil, flint glass, diamond.

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Convex Mirrors: Objects Closer Than They Appear

Convex mirrors produce a virtual, upright, and diminished image. The image appears closer than the actual object, making objects seem smaller and further away.

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Critical Angle

The critical angle is the angle of incidence at which a light ray passing from a denser medium to a less dense medium is refracted along the boundary between the two media.

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Angular Separation

The difference in angles between two refracted light rays of different wavelengths, like red and blue, when they enter a material.

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Convex Mirror

A mirror that curves outward, like the back of a spoon. It produces a smaller, virtual image that appears closer than the object.

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Polarizer

A material that allows only light waves vibrating in a specific direction to pass through. It blocks out all other directions of vibration.

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Dispersion of Light

The separation of white light into different colors, caused by variations in the refractive index of the medium for different wavelengths.

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Diffraction Grating

An optical component with many closely spaced parallel lines that diffracts light into different colors. More lines per cm mean greater sharpness.

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Double-Slit Experiment

Demonstrates the wave nature of light by creating interference patterns when light passes through two narrow slits. The spacing between the fringes depends on slit separation and wavelength.

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Refraction

The bending of light as it passes from one medium to another. Caused by changes in the speed of light in different media.

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Wavelength and Refractive Index

In most transparent materials, a higher refractive index means a higher frequency (shorter wavelength) of light.

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Converging Lens

A lens that causes parallel light rays to converge at a single point, the focal point. Has positive power.

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Liquid Crystal Display (LCD)

Screens that use liquid crystals, molecules that align themselves in response to electric fields, to control the passage of light and display images.

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Concave Mirror: Image Formation

A mirror that curves inward, like the inside of a spoon. It can produce real (inverted) or virtual (upright) images, depending on the object's position.

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Rayleigh Scattering

The scattering of electromagnetic radiation off particles much smaller than the wavelength of the radiation, which causes the sky to appear blue.

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Angle of Refraction

The angle between the refracted light ray and the normal to the surface, after light passes from one medium to another.

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Magnifying Glass Image

The image formed by a magnifying glass is always virtual, upright, and magnified.

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Refraction of Multiple Colors

When white light enters a medium like glass, different colors refract at slightly different angles, causing separation.

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Converging Lens Image (Inside Focal Point)

When an object is placed inside the focal point of a converging lens, the image is virtual, upright, and magnified.

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Destructive Interference

When two waves meet out of phase, they cancel each other out, resulting in darkness.

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Bragg's Law

A formula describing the conditions for constructive interference when X-rays are diffracted by a crystal lattice.

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Index of Refraction

A measure of how much a medium slows down light compared to its speed in a vacuum.

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Young's Double-Slit Experiment

A classic experiment demonstrating the wave nature of light. Two slits create an interference pattern on a screen.

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Distance between Slits

The distance between the two slits in Young's double-slit experiment determines the spacing of the interference pattern.

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In Phase (Light Waves)

Two light waves are in phase when their crests and troughs align, leading to constructive interference and increased brightness.

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Light Entering Different Media

When light enters a medium of different optical density, its speed and wavelength change, but its frequency remains constant.

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Virtual Image Magnification

The magnification of a virtual image formed by a lens is positive, indicating upright orientation.

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Bragg's Law (Higher Order)

The higher the order of the diffraction maximum (n), the larger the angle (theta) at which it occurs.

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Light Entering a Prism

The angle of incidence on a prism determines the direction of the emergent ray.

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Concave Mirror Reflection

Parallel rays reflecting off a concave mirror converge at the focal point.

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Refraction (Denser Medium)

When light travels from a less dense medium to a denser medium, it bends toward the normal.

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Light Speed in a Medium

Light travels slowest through materials with the highest index of refraction.

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Concave Mirror Magnification

The magnification of a concave mirror can be positive (upright image) or negative (inverted image) depending on the object's position.

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Concave Lens Image

Images formed by concave lenses can be either real or virtual. The image is real when the object is placed beyond the focal point, and virtual when placed within the focal point.

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Fiber Optics Phenomenon

Fiber optics utilize total internal reflection, where light travels within the fiber by repeatedly bouncing off the inner surface at angles greater than the critical angle.

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Oil Slick Colors: Cause

The colorful patterns on oil slicks are caused by interference of light waves reflecting off the top and bottom surfaces of the thin oil film.

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Concave Mirror: Center of Curvature

When an object is placed at the center of curvature of a concave mirror, the image is real, inverted, and the same size as the object.

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Double Concave Mirror: Image Location

An object placed at the center of curvature of a double concave mirror will have its image formed at the same location as the object, but it will be upright.

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Chromatic Aberration: Cause

Chromatic aberration occurs because different wavelengths of light have different speeds in a material. This results in different colors focusing at different points, causing a blurry image.

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Rainbow Formation

Rainbows are created by sunlight being refracted (bent) and dispersed (separated into colors) by water droplets, and then reflected back to the observer.

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Refractive Index & Chromatic Aberration

When the refractive index of the glass in a lens varies with wavelength, this leads to chromatic aberration because different colors will focus at different points.

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Total Internal Reflection: Condition

Total internal reflection occurs when light travels from a medium with a higher index of refraction to a medium with a lower index of refraction at an angle greater than the critical angle.

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Critical Angle in Glass-Water

The critical angle for light traveling from crown glass (n = 1.52) into water (n = 1.33) is approximately 61 degrees.

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Light Speed in Higher Index Medium

When light enters a material with a higher index of refraction, it slows down. This is because the material interacts more with the light, causing it to travel slower.

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What is another name for the POLARIZING ANGLE?

The polarizing angle, also known as Brewster's angle, is the angle at which unpolarized light incident on a surface becomes completely polarized, meaning it vibrates only in one direction.

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What type of aberration do spherical lenses have?

Spherical lenses suffer from spherical aberration, where light rays passing through different parts of the lens focus at slightly different points, leading to a blurry image.

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Diffraction Grating: Separation Between Orders

The separation between orders (brightness maxima) in a diffraction grating pattern depends on the slit spacing and the wavelength of light. Increasing the number of slits does not change the spacing between orders but improves sharpness.

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Which material has the slowest speed of light?

Diamond has the slowest speed of light among the given options - air, water, oil, flint glass, and diamond. This is because diamond has the highest refractive index.

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Why do rear-view mirrors say, ʺ OBJECTS IN MIRROR ARE CLOSER THAN THEY APPEAR.ʺ?

This warning indicates that the mirror is convex. Convex mirrors produce a virtual, upright, and diminished image, making objects appear smaller and further away than they actually are.

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Angle of Refraction in Glass

The angle at which light bends when passing from air into glass. This angle depends on the index of refraction of the glass.

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Magnifying Glass Image Orientation

The image formed by a magnifying glass is always upright, despite the magnification.

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Red & Blue Light Refraction

When red and blue light pass through glass, blue light bends more than red light, causing a separation in the emerging beams.

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Converging Lens: Object Inside Focal Point

If an object is placed within the focal point of a converging lens, the image formed is virtual, upright, and magnified.

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Critical Angle: Total Reflection

The angle of incidence at which a light ray passing from a denser medium to a less dense medium is totally reflected back into the denser medium.

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Destructive Interference: Path Difference

Destructive interference occurs when two waves meet out of phase, resulting in darkness. The path difference between the waves is a multiple of half a wavelength, m λ /2 where m=1, 3, 5, 7, ...

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Bragg's Law: X-Ray Diffraction

The condition 2d sin(θ) = n λ describes the angles at which X-ray beams are diffracted by a crystal lattice, creating interference patterns.

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Speed of Light in a Medium

The index of refraction (n) of a medium indicates the speed of light in that medium relative to its speed in a vacuum. The speed of light is slower in a medium with a higher index of refraction.

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Young's Double-Slit Experiment: Pattern

When light passes through two narrow slits, it creates an interference pattern on a screen, with alternating bright and dark bands.

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Two-Slit Experiment: Distance Between Slits

The distance between the two slits in Young's double-slit experiment determines the spacing between the bright fringes in the interference pattern.

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Light Waves In Phase

Two light waves are in phase when their crests and troughs align, leading to constructive interference and increased brightness.

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Bragg's Law: Higher Order Lines

Higher order diffraction maxima (n) appear at larger angles (θ) in X-ray diffraction patterns.

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Light Entering a Prism: Emergent Ray

The angle of incidence on a prism determines the direction of the emergent ray.

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Double-concave Mirror

A double-concave mirror has a curved surface that bulges outward on both sides. It always produces a virtual, upright, and diminished image, making objects appear smaller and farther away.

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Chromatic Aberration

Chromatic aberration is a type of optical distortion that occurs in lenses where different wavelengths of light (colors) focus at different points, resulting in a blurry image with colored fringes.

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Total Internal Reflection

Total internal reflection happens when light traveling in a denser medium (like water) strikes a boundary with a less dense medium (like air) at an angle greater than the critical angle. The light is then reflected back into the denser medium.

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Interference

Interference occurs when two or more waves overlap. If the waves are in phase, their amplitudes add up (constructive interference) and the wave is stronger. If they are out of phase, they partially or completely cancel each other out (destructive interference).

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What Happens to Light's Direction When It Enters a Denser Medium?

Light bends towards the normal when entering a denser medium. The normal is a line perpendicular to the surface at the point of incidence.

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What Happens to Light's Speed When It Enters a Less Dense Medium?

Light speeds up when it enters a less dense medium.

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What Kind of Lens Converges Light?

Converging lenses cause parallel light rays to converge at a single point, the focal point. They are also called convex lenses.

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What Kind of Mirror Creates a Smaller Image?

Convex mirrors create a smaller, virtual image that appears closer than the object. They curve outwards, like the back of a spoon.

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What Does 'Unpolarized' Light Mean?

Unpolarized light has electric fields vibrating in all possible directions. A polarizer filters out all but one direction of vibration.

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What Kind of Lens Has Positive Power?

A converging lens, also called a convex lens, has positive power. This means it causes light rays to converge.

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What is the Relationship Between Wavelength and Refractive Index?

In most transparent materials, a higher refractive index corresponds to a higher frequency (shorter wavelength) of light. This means shorter wavelengths bend more.

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What Happens to the Spacing of Interference Fringes When the Slit Separation is Cut in Half?

In a double-slit experiment, the distance between adjacent maxima (bright fringes) is inversely proportional to the slit separation. Cutting the slit separation in half doubles the distance between the fringes.

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What is Diffraction?

Diffraction is the spreading of light waves as they pass through an opening or around an obstacle. The amount of diffraction depends on the size of the opening or obstacle relative to the wavelength of light.

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What is a Double-Slit Experiment?

A classic experiment demonstrating the wave nature of light. Two slits create an interference pattern on a screen. The pattern shows bright and dark bands (maxima and minima).

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What is the Relationship Between the Number of Lines in a Diffraction Grating and the Dispersion?

A diffraction grating with more lines per centimeter produces a greater dispersion, meaning the colors are spread out more.

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Study Notes

Refraction and Reflection

  • An index of refraction less than 1 implies light travels faster in the medium than in a vacuum.
  • When light enters a material with a higher index of refraction, its speed decreases.
  • Brewster's angle is another name for the polarizing angle.
  • An index of refraction less than 1 for a medium means the speed of light in that medium is greater than the speed of light in a vacuum.

Lenses and Mirrors

  • Spherical lenses suffer from both spherical and chromatic aberration.
  • A concave shaving mirror with an erect image 1.5 times larger than the object, placed 30 cm in front, has a focal length of 20 cm.
  • Diffraction gratings with more slits (e.g., 4 slits) create better defined orders, not a greater separation between them, given the same slit separation.
  • Diamond has the slowest speed of light among the given options.
  • Rearview mirrors are usually convex, making objects appear closer than they actually are.
  • Light incident on a glass plate at 45° in air has a refraction angle less than 45° in the glass, dependent on the glass's refractive index.
  • A magnifying glass creates an image that may be the same orientation or upside-down, depending on the object's distance to the lens.
  • Light emerging from a rectangular glass plate separates with the blue beam displaced below the red beam if entering at an angle.
  • A converging lens with an object inside the focal point always creates a virtual image.
  • Total internal reflection occurs when the angle of incidence is greater than the critical angle, causing all light to be reflected.
  • Destructive interference occurs when the path difference is equal to mλ/2, where 'm' is an odd integer.
  • X-ray diffraction maxima follow Bragg's Law (2d sin θ = nλ).
  • The speed of light in a medium with an index of refraction of 1.5 is 2.0 x 108 m/s.

Interference and Diffraction

  • A double-slit experiment with monochromatic light produces alternating light and dark bands (interference pattern) on a screen.
  • In a two-slit experiment, the distance between slits can be calculated given the wavelength of light and the angle to the bright fringe.
  • Two light rays are in phase if their electric field strengths are maximum at the same time.
  • When light enters a medium with different optical density, its speed and wavelength change, but the frequency doesn't.
  • A virtual image magnified threefold by a lens with a 50 mm focal length requires the object to be placed 33.3 mm from it.
  • The second-order diffraction line for an X-ray beam with a 1.4 x 10-10 m wavelength and 20° angle is observed at 43°.

Mirrors, Prisms, and Polarisation

  • The light ray entering a prism obliquely will exit at an angle, depending on the prism and incident light's direction.
  • Parallel rays reflecting from a concave mirror intersect at the focal point.
  • Light traveling into a denser medium refracts toward the normal.
  • Light travels fastest in a vacuum.
  • A concave mirror with a focal length of 25 cm and an object 50 cm away has a magnification of -2.
  • Spherical mirrors suffer from spherical aberration.
  • The critical angle for a transparent material with a refractive index (n) is related to its critical angle (θc).
  • Reflection of light at a glass-air boundary results in a 180° phase change.
  • The refractive index of diamond (2.42) means light travels 2.42 times slower in the diamond than in a vacuum.
  • At diffraction maxima in a double-slit experiment, light waves from each slit arrive in phase.
  • Reflection at an air-glass boundary of light travelling in glass does not cause a phase change.

Additional Topics

  • The sky appears blue due to Rayleigh scattering.
  • The limiting angle of resolution for the eye is related to pupil diameter, light wavelength, and refractive index.
  • Images formed by concave lenses are always virtual, except at the focal point where they are real.
  • Fiber optics uses total internal reflection.
  • Oil slick colors are due to interference.
  • A concave mirror with an object at its center of curvature produces an inverted image of the same size.
  • A double-concave mirror at its center of curvature produces an image of the same size and upright.
  • Chromatic aberration arises from dispersion of light.
  • Rainbows are formed by refraction and dispersion of sunlight.
  • A lens with chromatic aberration has a refractive index that varies with wavelength.
  • Total internal reflection requires the incident angle to be in the medium with the higher refractive index.
  • The critical angle for crown glass to water boundary is 61°.
  • Light passing through a prism, the color refracted most, is violet.
  • Polarization of a light beam is defined by the vibrating direction of the electric field.
  • A converging meniscus lens with radii of curvature of 46 cm and n=1.60 will have a focal length of 36 cm.
  • Thin soap films appear black if very thin, reflecting no visible light.
  • The dispersion of a diffraction grating is greatest for a grating with more lines per centimeter.
  • In a two-slit experiment, if slit separation is halved, the distance between adjacent maxima doubles.
  • Light entering air from water refracts at an angle less than the incident angle.
  • As light frequency increases in common transparent media, the index of refraction increases.
  • A lens with a power of +10 Diopters and a first surface center of curvature in front is a convex meniscus.
  • Liquid Crystal Displays (LCDs) use polarization and dichroism.
  • Looking into a shiny spoon's convex side, creates a small, upright image.
  • When light passes between mediums, its direction and speed change.
  • Light travels fastest in a vacuum.
  • A shorter slit separation in a two-slit experiment leads to a wider separation of maxima on a screen.
  • Destructive interference and constructive interference are related to path differences, using wavelength as a factor. Constructive interference occurs when path differences are multiples of the light's wavelength and destructive interference occurs when they are multiples of the wavelength divided by two.

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