Optics

51. Which one of the following figures correctly shows the path of a ray o

Which one of the following figures correctly shows the path of a ray of light through a glass prism ?

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Image of path of light through prism
Image of path of light through prism
Image of path of light through prism
Image of path of light through prism
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UPSC NDA-2 – 2021
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Assuming Option A depicts the standard correct path of a ray of light through a glass prism. A ray of light entering a prism from air bends towards the normal upon entering the glass (denser medium). Inside the prism, it travels in a straight line. Upon exiting the prism from glass back into air (rarer medium), it bends away from the normal.
According to Snell’s Law, when light travels from a rarer medium (like air) to a denser medium (like glass), the ray bends towards the normal. When it travels from a denser medium to a rarer medium, it bends away from the normal. For a prism, the incident ray bends towards the normal at the first surface and the emergent ray bends away from the normal at the second surface. The net deviation of the ray is always towards the base of the prism for a ray entering one face and exiting another.
Different paths might be depicted in the options, such as bending away from the normal upon entry, no bending, total internal reflection, or bending towards the apex. Only one diagram correctly shows the path based on the principles of refraction. Without seeing the specific diagrams, it is assumed option A represents the correct standard path with deviation towards the base.

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52. Spherical mirror formula relating an object distance ‘u’, image distan

Spherical mirror formula relating an object distance ‘u’, image distance ‘v’ and focal length of mirror ‘f’ may be applied to a plane mirror when

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focal length goes to infinity.
focal length goes to zero.
image distance goes to zero.
image distance goes to infinity.
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The correct answer is A) focal length goes to infinity.
A plane mirror can be considered a spherical mirror with an infinitely large radius of curvature. Since the focal length of a spherical mirror is half its radius of curvature (f = R/2), the focal length of a plane mirror is also infinite.
The spherical mirror formula is 1/u + 1/v = 1/f. If f goes to infinity, then 1/f goes to zero. The formula becomes 1/u + 1/v = 0, which implies v = -u. This relationship (image distance is the negative of object distance, indicating a virtual image at the same distance behind the mirror as the object is in front) is consistent with the properties of a plane mirror.

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53. Power of a lens of focal length 25 cm is

Power of a lens of focal length 25 cm is

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+2-5 Dioptre
+3 Dioptre
+4 Dioptre
+5 Dioptre
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The correct answer is C) +4 Dioptre.
The power of a lens (P) is defined as the reciprocal of its focal length (f), when the focal length is expressed in meters. The formula is P = 1/f.
Given focal length f = 25 cm. Convert this to meters: 25 cm = 0.25 m.
Power P = 1 / 0.25 m = 1 / (1/4) m = 4 Dioptre (D).
A positive power indicates a converging (convex) lens.

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54. Twinkling of stars is primarily due to the atmospheric

Twinkling of stars is primarily due to the atmospheric

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refraction
reflection
polarization
dispersion
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The correct answer is A) refraction.
Twinkling of stars is caused by atmospheric refraction. As starlight passes through different layers of the Earth’s atmosphere with varying densities and temperatures, it undergoes repeated refraction in random directions, causing the apparent position and brightness of the star to fluctuate.
Planets, being much closer than stars, appear as extended sources rather than point sources. The total amount of light entering the eye from a planet remains relatively constant despite atmospheric refraction, which is why planets do not appear to twinkle.

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55. Tyndall effect is a phenomenon of

Tyndall effect is a phenomenon of

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scattering of light by the colloidal particles.
refraction of light by the colloidal particles.
dispersion of light by dust particles.
refraction of light by dust particles.
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The correct answer is A) scattering of light by the colloidal particles.
The Tyndall effect is the scattering of light as a light beam passes through a colloid. The individual suspension particles scatter and reflect light, making the beam visible.
This phenomenon is exhibited by colloidal solutions and fine suspensions, but not by true solutions. It is used to distinguish between a true solution and a colloidal solution. While dust particles can also scatter light, the term Tyndall effect is specifically associated with scattering by colloidal particles.

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56. Myopia is a defect in human vision where an image of a

Myopia is a defect in human vision where an image of a

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nearby object is focused beyond the retina.
nearby object is focused before the retina.
distant object is focused before the retina.
distant object is focused beyond the retina.
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The correct answer is C) distant object is focused before the retina.
Myopia, or nearsightedness, is a refractive error where light from distant objects is focused in front of the retina instead of directly on it. This results in distant objects appearing blurred.
In myopia, nearby objects are typically focused correctly on the retina (or even slightly behind, requiring less accommodation effort compared to a normal eye), which is why nearby vision is usually clear. Hyperopia (farsightedness) is when light is focused behind the retina.

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57. In case of a concave mirror, if an object is kept between principal fo

In case of a concave mirror, if an object is kept between principal focus F and pole P of the mirror, then which one of the following statements about the image is NOT correct ?

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The image will be virtual
The image will be enlarged or magnified
The image will be formed at infinity
The image will be erect
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The statement “The image will be formed at infinity” is NOT correct.
When an object is placed between the principal focus (F) and the pole (P) of a concave mirror, the reflected rays diverge but appear to originate from a point behind the mirror. This forms a virtual image.
For a concave mirror with an object between F and P:
– The image is formed behind the mirror.
– The image is virtual (cannot be projected on a screen).
– The image is erect (upright relative to the object).
– The image is magnified (larger than the object).
An image is formed at infinity by a concave mirror only when the object is placed exactly at the principal focus (F). When the object is between F and P, the image is virtual and located at a finite distance behind the mirror.

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58. The refractive index of fused quartz is 1.46 and that of sapphire is 1

The refractive index of fused quartz is 1.46 and that of sapphire is 1.77. If vq is the speed of light in quartz and vs is the speed of light in sapphire, then which one of the following relations is correct ?

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”v<sub>q</sub>
”v<sub>s</sub>
”v<sub>s</sub>
”v<sub>s</sub>
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The relation vq > vs is correct.
The refractive index (n) of a medium is inversely proportional to the speed of light (v) in that medium, according to the formula n = c/v, where c is the speed of light in a vacuum. Therefore, v = c/n. A higher refractive index means a lower speed of light, and a lower refractive index means a higher speed of light.
Given nq = 1.46 and ns = 1.77. Since ns > nq, it follows that vs = c/ns must be less than vq = c/nq. Hence, vq > vs. The speed of light is slower in sapphire than in fused quartz because sapphire has a higher refractive index.

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59. A lens has a power of +2.0 Dioptre. Which one of the following stateme

A lens has a power of +2.0 Dioptre. Which one of the following statements about the lens is true ?

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The lens is concave and has a focal length of 0.5 metre
The lens is convex and has a focal length of 2.0 metre
The lens is convex and has a focal length of 0.5 metre
The lens is concave and has a focal length of 2.0 metre
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The correct answer is (C) The lens is convex and has a focal length of 0.5 metre.
The power of a lens (P) is the reciprocal of its focal length (f) when the focal length is measured in meters. The formula is P = 1/f. Given the power P = +2.0 Dioptre, the focal length f = 1/P = 1/2.0 = 0.5 meters. A positive power indicates a converging lens, which is a convex lens.
Concave lenses have negative power and diverge light. Convex lenses have positive power and converge light (for real objects). The unit of power is Dioptre (D), where 1 D = 1 m⁻¹.

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60. The Sun appears reddish during sunrise and sunset. The phenomenon in o

The Sun appears reddish during sunrise and sunset. The phenomenon in optics which is responsible for this appear-ance of the Sun is

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Reflection
Total internal reflection
Scattering
Interference
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The correct answer is (C) Scattering.
The phenomenon responsible for the reddish appearance of the Sun during sunrise and sunset is the scattering of sunlight by particles in the Earth’s atmosphere, primarily Rayleigh scattering. When the Sun is near the horizon, sunlight passes through a much longer path in the atmosphere. Shorter wavelengths of light (blue, violet) are scattered away more effectively than longer wavelengths (red, orange). As a result, the light that reaches our eyes after travelling through this longer path is enriched with longer wavelengths, making the Sun and the sky around it appear reddish.
Reflection is the bouncing of light off a surface. Total internal reflection occurs when light travelling in a denser medium hits a boundary with a less dense medium at a large angle. Interference occurs when waves overlap and combine, leading to reinforcement or cancellation. While these are optical phenomena, scattering is the specific one responsible for the sky’s colour and the reddish hues of the sun at sunrise/sunset.

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