Questions and Answers
What makes objects visible in a dark room?
Light
Light travels in straight lines only.
False
What is a concave mirror?
What is the principal focus of a concave mirror?
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What is the relationship between the radius of curvature and the focal length for spherical mirrors?
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Where is the center of curvature of a concave mirror located?
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The size of an image formed by a plane mirror is __________.
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What happens to the image when the object is placed at the principal focus of a concave mirror?
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Define the principal focus of a concave mirror.
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What is the focal length of a spherical mirror with a radius of curvature of 20 cm?
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Name a mirror that can give an erect and enlarged image of an object.
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Why do we prefer a convex mirror as a rear-view mirror in vehicles?
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Find the focal length of a convex mirror whose radius of curvature is 32 cm.
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A concave mirror produces a three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Where is the image located?
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The distance of the image from the pole of the mirror is called the _____ distance.
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The height of the image should be taken as positive for _____ images.
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Which of the following mirrors produces a real, inverted image?
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What happens to light rays when they hit a concave mirror?
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When a ray of light traveling in air enters obliquely into water, does the ray bend towards the normal or away from the normal? Why?
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Light enters from air to glass having a refractive index of 1.50. What is the speed of light in the glass if the speed of light in vacuum is $3 \times 10^8$ m/s?
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From Table 10.3, what is the medium having the highest optical density? Also, what is the medium with the lowest optical density?
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In which of the following mediums does light travel fastest: kerosene, turpentine, or water?
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What is the meaning of a refractive index of diamond being 2.42?
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What type of lens converges light rays?
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What type of lens diverges light rays?
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What is the principal focus of a lens?
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What does the focal length of a lens represent?
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Define 1 dioptre of power of a lens.
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Where is the needle placed in front of the convex lens if the image is equal to the size of the object at a distance of 50 cm?
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What is the power of a concave lens of focal length 2 m?
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Which one of the following materials cannot be used to make a lens?
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Where should the object be placed for a virtual, erect image larger than the object using a concave mirror?
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Where should an object be placed in front of a convex lens to get a real image the size of the object?
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What type of lenses have a focal length of -15 cm?
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What type of mirror will always result in an erect image regardless of distance from the mirror?
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Which lens would be preferred for reading small letters in a dictionary?
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What should be the range of distance of the object from a concave mirror of focal length 15 cm to obtain an erect image?
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What is the nature of the image formed by a concave mirror when the object is between its focal point and mirror?
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Is the image larger or smaller than the object when using a concave mirror in this case?
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Name the type of mirror used in car headlights.
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Name the type of mirror used in side/rear-view mirrors of vehicles.
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Name the type of mirror used in a solar furnace.
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Will a convex lens that is half-covered with black paper produce a complete image of the object?
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What is the position of an image formed by a concave lens of focal length 15 cm when the image is 10 cm from the lens?
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What is the position and nature of the image when an object is placed at a distance of 10 cm from a convex mirror with a focal length of 15 cm?
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What does a magnification of +1 mean in the context of a plane mirror?
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Find the position of the image, its nature, and size for an object of length 5 cm placed at a distance of 20 cm in front of a convex mirror with a radius of curvature of 30 cm.
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At what distance from a concave mirror of focal length 18 cm should a screen be placed to obtain a sharp focused image if the object is 27 cm in front?
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What is the focal length of a lens with a power of -2.0 D?
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Find the focal length of a corrective lens with a power of +1.5 D. Is it diverging or converging?
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Study Notes
Light - Reflection and Refraction
- Objects are visible due to light reflection; visible in illuminated conditions.
- Light travels in straight lines, evidenced by sharp shadows cast by opaque objects.
- Diffraction occurs when light bends around small obstacles; wave theory explains light's behavior in such cases.
- Wave-particle duality: light exhibits properties of both waves and particles, reconciled by modern quantum theory.
Reflection of Light
- Highly polished surfaces, like mirrors, reflect most incident light.
- Laws of reflection:
- Angle of incidence equals angle of reflection.
- Incident ray, normal at the point of incidence, and reflected ray lie in the same plane.
- Plane mirror images:
- Always virtual and erect.
- Same size as the object.
- Image distance equals object distance.
- Images are laterally inverted.
Spherical Mirrors
- Curved mirrors classified as concave (inward curving) or convex (outward curving).
- Key terms related to spherical mirrors:
- Pole (P): Point on the mirror's surface.
- Centre of curvature (C): Centre of the sphere from which the mirror is a segment; lies outside the mirror.
- Radius of curvature (R): Distance from the pole to the centre of curvature.
- Principal axis: Straight line through the pole and centre of curvature, perpendicular to the mirror's surface.
- Focal length (f): Distance from the pole to the principal focus (F); related by R = 2f for small-aperture mirrors.
Image Formation by Spherical Mirrors
- Image properties depend on object position relative to points P, F, and C.
- Possible image characteristics for concave mirrors:
- At infinity: Real, inverted, point-sized image at focus.
- Beyond C: Real, inverted, diminished image between F and C.
- At C: Real, inverted, same size image at C.
- Between C and F: Real, inverted, enlarged image beyond C.
- At F: Real, inverted, highly enlarged image at infinity.
- Between P and F: Virtual, erect, enlarged image behind the mirror.
Ray Diagrams for Image Formation
- Two key rays used to locate images:
- Ray parallel to the principal axis reflects through the focus (concave) or appears to diverge from focus (convex).
- Ray through the focus reflects parallel to the principal axis.
- Ray through the centre of curvature is reflected back along the same path.
- Ray hitting the pole reflects at equal angles of incidence and reflection.
Activities for Understanding
- Experiment with a concave mirror to observe image formation and find focal length through sunlight concentration.
- Construct ray diagrams for various object positions relative to a concave mirror to understand image properties visually and conceptually.### Uses of Concave Mirrors
- Concave mirrors produce powerful parallel light beams; common in torches, search lights, and vehicle headlights.
- Used in shaving mirrors for an enlarged view of the face.
- Dentists utilize concave mirrors to obtain larger images of patients' teeth.
- Large concave mirrors concentrate sunlight to generate heat in solar furnaces.
Image Formation by Convex Mirrors
- Convex mirrors create upright and diminished images, regardless of the object's position.
- When an object is located at infinity, the image forms at the focus behind the mirror and is point-sized.
- An object between infinity and the pole produces a diminished virtual image located between the focus and the mirror.
Observing Image Formation
- Activities demonstrate image properties in convex mirrors, showing images are diminished and always virtual.
- Convex mirrors provide a full-length view of tall objects due to their wide field of vision.
- Uniquely positioned convex mirrors, as seen in Agra Fort, allow for full-length images of tall buildings or tombs.
Uses of Convex Mirrors
- Commonly used as rear-view mirrors in vehicles.
- Provide an erect, diminished image and a broader field of view compared to plane mirrors.
Sign Convention for Spherical Mirrors
- The pole of the mirror is the origin for distance measurements.
- Object is placed to the left; distances along the principal axis to the right are positive, and to the left are negative.
- Heights above the principal axis are positive; below are negative.
Mirror Formula and Magnification
- The mirror formula relates object distance (u), image distance (v), and focal length (f):
- ( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} )
- Magnification (m) measures image size relative to object size, expressed as:
- ( m = \frac{h'}{h} = \frac{v}{u} )
- Positive magnification indicates a virtual image, while negative indicates a real image.
Example Calculations for Mirrors
- Convex mirror example with radius of curvature 3.00 m, yielding a focal length of 1.50 m.
- Image distance calculated from the mirror formula indicates a virtual and diminished image.
- Concave mirror example demonstrates finding image distance and nature using the mirror formula with specific object size and position.
Refraction of Light
- Refraction occurs when light passes from one medium to another, altering its path.
- Common experiences, such as an object appearing raised in water, illustrate the effects of refraction.
- Light shifts direction when entering different mediums, with varying effects based on the medium's refractive indices.
Laws of Refraction
- Incident, refracted ray, and normal lie in the same plane.
- Snell's law relates the angle of incidence to angle of refraction through constant ratios:
- ( \frac{\sin i}{\sin r} = \text{constant} )
Refractive Index
- A measure of how light travels at different speeds in various media.
- Highest speed of light is in a vacuum, followed by air, and significantly slower in water or glass.
- The refractive index quantifies speed changes between two media.### Refractive Index
- The refractive index ( n_{21} ) of medium 2 with respect to medium 1 is the ratio of the speed of light in medium 1 (( v_1 )) to that in medium 2 (( v_2 )).
- The formula: ( n_{21} = \frac{v_1}{v_2} ).
- Conversely, the refractive index ( n_{12} ) of medium 1 with respect to medium 2 is expressed as: ( n_{12} = \frac{v_2}{v_1} ).
- The absolute refractive index ( n_2 ) of a medium, when medium 1 is vacuum or air, is given by: ( n_m = \frac{c}{v} ), where ( c ) is the speed of light in air.
- Values for refractive indices of various materials include:
- Water: ( n_w = 1.33 )
- Crown glass: ( n_g = 1.52 )
- Diamond: ( n_d = 2.42 )
Optical Density
- Optical density refers to a medium's ability to refract light, not to be confused with mass density.
- A medium with a higher refractive index is considered optically denser.
- Light travels faster in a rarer medium than in a denser medium, bending towards the normal when entering a denser medium.
Lenses
- Lenses are transparent materials with at least one spherical surface.
- Types of lenses:
- Convex Lens (Converging): Thicker in the middle, converges light rays.
- Concave Lens (Diverging): Thinner in the middle, diverges light rays.
- Principal focus is where parallel rays converge (convex) or appear to diverge from (concave).
- Focal length ( f ) is the distance from the optical center to the principal focus.
Image Formation by Lenses
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Convex lenses can form images based on the object's position:
- At infinity: Image at focus ( F_2 ), highly diminished.
- Beyond ( 2F_1 ): Image between ( F_2 ) and ( 2F_2 ), diminished.
- At ( 2F_1 ): Image at ( 2F_2 ), same size.
- Between ( F_1 ) and ( 2F_1 ): Image beyond ( 2F_2 ), enlarged.
- At focus ( F_1 ): Image at infinity, highly enlarged.
- Between focus and optical center: Virtual and erect image.
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Concave lenses always produce virtual, erect, and diminished images, regardless of the object's position.
Ray Diagrams and Sign Convention
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Ray diagrams represent light refraction through lenses.
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For drawing ray diagrams:
- Parallel rays through a convex lens converge at focus.
- Rays through focus in a convex lens exit parallel.
- Rays through the optical center pass without deviation.
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Sign convention for lenses:
- Focal length of convex lenses is positive, while that for concave lenses is negative.
- Measurements are based on the optical center of the lens, affecting signs for object distance ( u ), image distance ( v ), and heights ( h ) and ( h' ).
Lens Formula and Magnification
- There exists a lens formula similar to spherical mirrors, allowing calculations of image properties.
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Description
Explore the fascinating concepts of light in Chapter 10, focusing on the principles of reflection and refraction. Understand how light interacts with objects, enabling visibility and the formation of images. This chapter is essential for grasping the foundational aspects of optics.
