Geometrical optics basics
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Questions and Answers

In geometrical optics, which property of light is primarily considered?

  • Polarization of light waves.
  • The travel of light as rays in straight lines. (correct)
  • Diffraction of light around obstacles.
  • Interference patterns formed by light waves.

What causes a solar eclipse?

  • The combined shadows of Earth and Moon.
  • The Moon's shadow falling on the Earth. (correct)
  • The Earth's shadow falling on the Moon.
  • The Sun passing behind the Earth.

What distinguishes a virtual image from a real image?

  • A real image is always upright, while a virtual image is inverted.
  • A real image is formed by the actual convergence of light rays; a virtual image is not. (correct)
  • A virtual image can be projected on a screen, while a real image cannot.
  • A virtual image is formed by the actual convergence of light rays; a real image is not.

If an object is placed 2 meters in front of a plane mirror, where does the virtual image appear to be located?

<p>2 meters behind the mirror. (A)</p> Signup and view all the answers

What is a key characteristic of the image formed by a plane mirror related to its orientation?

<p>The image is laterally inverted. (A)</p> Signup and view all the answers

What is the relationship between the angle of incidence and the angle of reflection for a ray of light striking a smooth surface of a plane mirror?

<p>The angle of incidence is equal to the angle of reflection. (D)</p> Signup and view all the answers

In the context of shadows formed during eclipses, what is the difference between the umbra and penumbra?

<p>The umbra is the completely dark region, while the penumbra is partially shaded. (C)</p> Signup and view all the answers

Which of the following best describes why the study of shadows is relevant to geometrical optics?

<p>Shadows illustrate how light travels in straight lines and is obstructed by objects. (A)</p> Signup and view all the answers

Why do satellite dishes using microwaves function effectively even with a wire mesh surface?

<p>Microwaves have much larger wavelengths compared to visible light, allowing them to reflect off a less smooth surface. (D)</p> Signup and view all the answers

What is the primary requirement for a mirror's surface to reflect light properly and form a clear image?

<p>The surface must be extremely smooth, with roughness significantly smaller than the wavelength of visible light. (A)</p> Signup and view all the answers

Under what condition does a partially silvered mirror create images in the same location, regardless of the light source’s position?

<p>Partially silver mirrors always create images at the same location for any light source position. (B)</p> Signup and view all the answers

What is the key characteristic used to differentiate between real and virtual images formed by mirrors and lenses?

<p>The apparent origin of the light rays when traced backward. (C)</p> Signup and view all the answers

If visible light has a wavelength ranging from 4000 to 7000 Å, what is the ideal surface roughness for a mirror to ensure accurate reflection and maintain the equality of the angles of incidence and reflection?

<p>Roughness should be at least eight times smaller than the wavelength of light. (B)</p> Signup and view all the answers

Suppose you have a bi-convex lens and a light source. How does the bi-convex lens contribute to the formation of an image?

<p>It bends the light rays, causing them to converge at a point, forming an image. (A)</p> Signup and view all the answers

An object is placed 10 cm in front of a plane mirror. How far behind the mirror will the image appear to be located?

<p>10 cm (A)</p> Signup and view all the answers

In the context of image formation with mirrors and lenses, what does it mean for light rays to 'converge'?

<p>The light rays meet at a single point. (A)</p> Signup and view all the answers

Chromatic aberration is corrected by applying specialized coatings to lenses. What does this minimize?

<p>The difference in focal points for various colors of light. (A)</p> Signup and view all the answers

How does reducing the aperture of a lens minimize spherical aberration?

<p>It blocks the more divergent rays, allowing parallel rays to converge more effectively. (C)</p> Signup and view all the answers

A convex lens is held close to an object and then moved away. What happens to the apparent size of the object, until it eventually defocuses?

<p>The object appears to get larger, until it defocuses. (D)</p> Signup and view all the answers

What does '$f$' represent in the magnification formula $m_\theta = \frac{25 \text{cm}}{f}$ for a simple magnifier?

<p>The focal length of the lens. (A)</p> Signup and view all the answers

What is the standard closest distance at which the human eye can focus comfortably?

<p>25 cm (C)</p> Signup and view all the answers

Why is there a practical limit to the magnification achievable with a single lens?

<p>Too short a focal length can cause aberrations. (B)</p> Signup and view all the answers

In a compound microscope, what is the role of the objective lens?

<p>To create an intermediate image that the eyepiece then magnifies. (B)</p> Signup and view all the answers

For a concave mirror, where must an object be placed to produce a real image that is smaller than the object?

<p>Beyond the center of curvature (C). (D)</p> Signup and view all the answers

In a compound microscope, if the height of the object is 'h' and the height of the intermediate image formed by the objective lens is 'h’', what does the eyepiece lens then do?

<p>It magnifies the intermediate image of height h'. (B)</p> Signup and view all the answers

In the context of mirrors, what does the magnification factor describe?

<p>The ratio of the image height to the object height. (D)</p> Signup and view all the answers

A pencil is placed in front of a convex mirror. Which of the following best describes the image formed?

<p>Virtual, upright, and diminished. (B)</p> Signup and view all the answers

What happens to a P-ray (parallel ray) after it strikes a concave mirror?

<p>It reflects through the focal point. (D)</p> Signup and view all the answers

Why do convex mirrors produce virtual images?

<p>Because the reflected rays diverge, and their extensions converge behind the mirror. (D)</p> Signup and view all the answers

If an object is placed between the center of curvature (C) and the focal point (F) of a concave mirror, which of the following describes the image formed?

<p>Real, inverted, and larger than the object. (D)</p> Signup and view all the answers

What is the relationship between the focal length (f) and the radius of curvature (R) for a convex mirror?

<p>$f = -R/2$ (A)</p> Signup and view all the answers

Which type of mirror is commonly used in applications like shaving mirrors due to its magnification properties?

<p>Concave mirror. (C)</p> Signup and view all the answers

How does the reflective surface of a concave mirror differ from that of a convex mirror?

<p>A concave mirror has a reflective surface on the inner side of the spherical section, while a convex mirror has it on the outer side. (A)</p> Signup and view all the answers

A light source is placed at various distances from a concave mirror. What happens to the clarity of the image formed on a screen as the mirror is brought closer to the light source?

<p>The image clarity improves, reaches a specific position of maximum clarity, and then becomes blurry again. (B)</p> Signup and view all the answers

What is the significance of the focal point (F) in relation to a concave mirror?

<p>The focal point is the point where parallel light rays converge after reflecting off the mirror. (D)</p> Signup and view all the answers

For a concave mirror, how is the focal length related to the radius of curvature (R)?

<p>The focal length is half the radius of curvature (F = R/2). (D)</p> Signup and view all the answers

How does the focal point of a convex mirror differ from that of a concave mirror, and what is the sign convention associated with it?

<p>A convex mirror appears to have a virtual focal point behind it, while a concave mirror has a real focal point in front of it; convex mirrors have a negative focal length. (A)</p> Signup and view all the answers

Consider a P-ray and F-ray interacting with a concave mirror. Which of the following statements accurately describes their behavior?

<p>The P-ray travels parallel to the axis, reflects through the focal point, and the F-ray strikes the focal point, reflects parallel to the axis. (D)</p> Signup and view all the answers

An object is placed at the focal point of a concave mirror. Where will the reflected rays appear to converge?

<p>The reflected rays will be parallel and will not converge. (D)</p> Signup and view all the answers

In the context of spherical mirrors, what does the term 'virtual focus' refer to?

<p>The point from which parallel light rays appear to originate after reflecting off a convex mirror. (D)</p> Signup and view all the answers

What key condition is necessary for total internal reflection to occur within a prism?

<p>The angle of incidence must exceed the critical angle. (C)</p> Signup and view all the answers

In what way do prisms contribute to the functionality of binoculars?

<p>By correcting the orientation of the image and extending the optical path. (D)</p> Signup and view all the answers

How can prisms act as mirrors, and what is a significant advantage of this application?

<p>Through total internal reflection; it eliminates the need for reflective coatings. (D)</p> Signup and view all the answers

What phenomenon, predicted by Einstein's theory of general relativity, causes light to bend in space?

<p>Gravitational lensing. (C)</p> Signup and view all the answers

How does gravitational lensing enable us to study distant objects like quasars?

<p>By magnifying and focusing the light from these objects, making them visible. (C)</p> Signup and view all the answers

Consider a prism with a known refractive index. If light strikes one of its surfaces at an angle of incidence greater than the critical angle, what will occur?

<p>The light will undergo total internal reflection and remain within the prism. (B)</p> Signup and view all the answers

Imagine binoculars redesigned without prisms. What adjustments would be necessary to maintain the same magnification and image orientation?

<p>More complex lens arrangements would be needed to correct image orientation, significantly lengthening the binoculars. (D)</p> Signup and view all the answers

A distant star's light is observed to bend significantly as it passes near a supermassive black hole. What does this observation confirm, according to physics?

<p>Einstein's theory of general relativity, where gravity bends light. (A)</p> Signup and view all the answers

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Flashcards

Geometrical Optics

The study of light as rays traveling in straight lines, disregarding wave properties like interference and diffraction.

Shadow

A dark area formed when an object blocks light; has a completely dark region and a partially dark region.

Solar Eclipse

An eclipse where the moon blocks the sun's light, casting a shadow on the Earth.

Lunar Eclipse

An eclipse where the Earth blocks the sun's light, casting a shadow on the Moon.

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Virtual Image

An image formed where light rays appear to converge, but do not actually do so.

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Plane Mirror

A mirror that reflects light in such a way that the virtual image appears behind the mirror's surface.

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Angle of Incidence = Angle of Reflection

Light rays reflect off a smooth surface at the same angle they hit it.

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Real Image

An image formed when light rays actually converge at a point.

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Spherical Mirrors

Curved mirrors created by cutting a sphere and coating the surface with a reflective material.

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Concave Mirror

A mirror where the reflective surface is the inner surface of a sphere.

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Convex Mirror

A mirror where the reflective surface is the outer surface of a sphere.

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Focal Point (F)

The point where parallel light rays converge after reflecting off a concave mirror.

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Focal Length

The distance from the center of the mirror to the focal point (R/2).

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Virtual Focus

The point from which parallel light rays appear to originate after reflecting off a convex mirror.

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P-ray

A light ray that travels parallel to the axis and reflects through the focal point.

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F-ray

A light ray that strikes the focal point and reflects parallel to the axis.

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Diffuse Reflection

Reflection where light rays scatter in many directions, preventing a clear image.

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Specular Reflection

Reflection off a smooth surface where light rays maintain their angle of incidence and reflection, creating a clear image.

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Mirror Surface Smoothness

For a mirror to properly reflect visible light (4000-7000 Å), its surface roughness should be significantly smaller (ideally 8x smaller).

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Satellite Dish Reflection

Uses microwaves with large wavelengths, so a wire mesh (less smooth surface) is still effective for reflection.

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Bi-Convex Lens

A lens bends light rays to converge at a point, forming an image.

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Partially Silvered Mirror

Allows light to both reflect and pass through, creating images in the same location regardless of the source position.

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Object-Image Distance in Mirrors

The distance from the object to the mirror is the same as the distance from the mirror to the image.

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Concave Mirror: Object beyond C

If an object is placed beyond C, the image will be real and smaller.

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Concave Mirror: Object between C and F

If the object is between C and F, the image will be real and larger.

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Magnification Factor

Ratio of image height to object height; also equals -q/p, where q is image distance and p is object distance.

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Convex Mirror: Image Formation

Rays diverge, forming a virtual, upright, and diminished image behind the mirror.

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Convex Mirrors: Reflected Light

The reflected rays diverge

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Chromatic Aberration

Blurriness caused by different colors of light converging at different focal points.

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Spherical Aberration

Distortion from rays striking different parts of a lens not converging at a single point.

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Angular Magnification

Ratio of the angle subtended by the image to the angle subtended by the object at the eye.

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Near Point

The shortest distance at which the eye can focus comfortably, typically 25cm.

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Simple Magnifier

Uses a single convex lens to magnify objects.

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Compound Microscope

Optical instrument using two lenses (objective and eyepiece) to achieve high magnification.

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Objective Lens

The first lens in a compound microscope, which creates an initial magnified image.

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Eyepiece Lens

The second lens in a compound microscope, which further magnifies the image from the objective lens.

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Prisms

Optical devices that disperse light and enable total internal reflection.

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Total Internal Reflection

The complete reflection of light within a material when the incident angle exceeds a critical angle.

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Prism use in Binoculars

Prisms extend the optical path in a compact space using total internal reflection.

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Prisms as Mirrors

Using total internal reflection, prisms can act as mirrors without reflective coatings.

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Gravitational Lensing

The bending of light around massive objects due to gravity, predicted by Einstein.

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Purpose of Gravitational Lensing

Allows observation of distant objects, like quasars, by focusing their light with massive celestial bodies.

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Image Inversion by Prism

Phenomenon where an image becomes inverted when a prism is rotated.

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Critical Angle

The minimum angle of incidence at which total internal reflection occurs.

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Study Notes

  • Geometrical optics studies light as rays traveling in straight lines, disregarding wave properties like interference and diffraction.
  • Light obstructed by an object casts shadows in the opposite direction of the light source.
  • Shadows consist of a completely dark region and a partially dark region.
  • Solar eclipses happen when the moon blocks the sun's rays, casting a shadow on Earth.
  • Lunar eclipses occur when Earth blocks the sun's rays, casting a shadow on the moon.

Reflection and Mirrors

  • A virtual image is a reflection seen in a mirror, formed by light rays bouncing off the mirror.
  • Reflected rays appear to converge behind the mirror, but do not physically do so.
  • A virtual image appears to be the same distance behind the mirror as the object is in front.
  • Virtual images are upright and the same size as the object, but laterally inverted (left and right are switched).
  • A mirror reflects light such that a virtual image seems to exist behind its surface.
  • A virtual image forms where extended rays appear to converge, while a real image forms when light rays converge at a point.
  • The angle of incidence equals the angle of reflection in a plane mirror.
  • A smooth mirror surface ensures light rays reflect symmetrically, while a rough surface causes light to scatter and prevents clear image formation.
  • To reflect light properly, a mirror's surface should be extremely smooth, with roughness ideally eight times smaller than the wavelength of visible light (4000 to 7000 Å).
  • Satellite dishes use microwaves with larger wavelengths, and can function effectively with a less smooth surface

Lenses and Image Formation

  • A biconvex lens bends light, causing rays from a light source to converge and form an image.
  • Partially silvered mirrors can reflect and pass light, creating images at the same location regardless of the source's position.
  • To determine if an image is real or virtual, trace light rays backward, if rays emanate the image is virtual, if they converge it is real.
  • The distance from an object to a mirror equals the distance from the mirror to the virtual image.

Spherical Mirrors

  • Curved mirrors can be created by cutting a sphere and coating it with a reflective material.
  • Concave and convex mirrors are formed based on whether the inner or outer surface is coated, each with different reflective properties.
  • Concave mirrors produce different images of surrounding lights on a screen based on the distance the mirror sits from the surrounding object.
  • Parallel light rays striking a concave mirror converge at the focal point (F), located R/2 from the center of the mirror, known as the focal length.
  • Parallel light rays striking a convex mirror appear to originate from a virtual focus behind the mirror.
  • Focal length is negative if the focus is behind the mirror (convex), and positive (R/2) if in front (concave).

Image Formation in Concave Mirrors

  • P-ray travels parallel to the axis and reflects through the focal point.
  • F-ray strikes the focal point and reflects parallel to the axis.
  • C-ray passes through the center and reflects back on itself.
  • When an object is placed beyond the center (C), reflected rays form a smaller, real image.
  • When an object is placed between the center (C) and the focal point (F), reflected rays form a larger, real image.

Magnification

  • Magnification factor is the ratio of image size (h') to object size (h), expressed as h'/h or -q/p.
  • q is the distance from the mirror to the image, and p is the distance between the object and the mirror.

Image Formation in Convex Mirrors

  • Reflected rays diverge
  • Extending the reflected rays backward shows a virtual image is formed
  • Convex mirrors produce diminished, upright images, and their images remain upright.
  • Focal length for a convex mirror is -R/2, since the image formed is virtual

Refraction and Lenses

  • Lenses focus or disperse light due to changes in speed caused by the difference in refractive index.
  • Refractive index (n) is the ratio of the speed of light in a vacuum to its speed in a medium.
  • Light bends towards normal when entering a lens due to refraction.
  • Convex lenses converge light, while concave lenses diverge light.
  • Parallel light rays converge at a point in a convex lens.

Lensmaker's Equation and Lens Types

  • The focal length of a spherical lens is determined by the lensmaker's formula, accounting for the lens's curvature: 1/f = (n-1) * (1/R1 - 1/R2).
    • n is the refractive index
    • R1 and R2 are radii of curvature for the lens surfaces
  • R2 is considered negative when the lens curves inward from the light source.
  • Different lens shapes include biconvex, biconcave, plano-convex, and plano-concave.

Diopter

  • Diopter is the reciprocal of a lens's focal length (f) in meters (Diopter = 1/f).
  • A lens with greater power can focus or diverge light more effectively. For a convex lens, the image formed is always inverted.

Image Formation with Lenses

  • Close objects appear magnified and virtual with convex lenses as the light rays diverge.
  • Objects move away from the lens and then become smaller and real as light rays converge to a point.
  • Concave lenses produce smaller, virtual images by diverging light rays.

Lens Defects

  • Chromatic aberration has different colors focusing at different points.
  • Spherical aberration has rays striking different parts of a wide lens not converging at a single point.

Optical Instruments

  • reducing the lens's aperture minimizes aberration
  • Parallel rays converge more effectively to produce a clearer image.
  • The simple magnifier causes the image to be normal size when held close, and grows larger until it defocuses when moved away.

The Ratio of Theta Prime to Theta

  • The ratio describes magnification: m = (θ'/θ) = (h/f) / (h/25cm) = 25cm/f.
  • 25 cm is the typical closest distance at which the human eye can focus comfortably.

Compound Microscope

  • Microscopes magnify objects using two lenses: the objective and the eyepiece.
  • Light rays form an intermediate image which is then magnified by he eyepiece lens, resulting in a larger final image.

Total Magnification

  • M = mo * me = (-s/fob) * (25cm/fey)
    • M = total magnification
    • fob = focal length of the objective lens
    • fey = focal length of the eyepiece
    • s = tube length
  • The negative sign indicates that the intermediate image is inverted.

Refracting Telescope

  • The telescope increases the angle of view to make distant objects appear closer and larger The objective leans captures the objects at a distance.

Human Eye

  • Light focuses precisely on the retina to create a clear image.

Eye Defects

  • Farsightedness (hypermetropia) has difficulty seeing near objects.
  • Farsightedness is corrected using a convex lens.
  • Nearsightedness (myopia) has difficulty seeing distant objects.
  • Nearsightedness is corrected using a concave lens.

Prisms

  • Prisms are used for total internal reflection.
  • Internal reflection happens when the angle of incidence exceeds a critical values
  • Reflecting internally causes an image to be the same size as the object
  • Rotating the prism inverts the image.
  • Prisms extend the optical path without increasing physical length.
  • Prisms can be mirrors through the phenomenon of total internal reflection without needing a coating.

Advanced optics

  • Gravitational lensing bends light due to gravity from massive objects, allowing to observe distant objects like quasars.

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Description

Explore the fundamental principles of geometrical optics. This includes reflection, image formation, and the behavior of light with mirrors. Understand concepts such as real vs. virtual images, umbra and penumbra, and the properties of plane mirrors.

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