Optics Archives

111. The Sun is seen little before it rises and for a short while after it

The Sun is seen little before it rises and for a short while after it sets. This is because of

[amp_mcq option1=”total internal reflection” option2=”atmospheric refraction” option3=”apparent shift in the direction of Sun” option4=”dispersion” correct=”option2″]

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UPSC NDA-1 – 2019

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The phenomenon of seeing the Sun slightly before it rises and after it sets is caused by atmospheric refraction.

– Light from the Sun bends as it passes through the Earth’s atmosphere, which is denser near the surface.
– When the Sun is below the horizon, the light rays from it are refracted (bent) downwards as they enter the atmosphere, making the Sun appear to be above the horizon to an observer.
– This effect causes the Sun to be visible for a few minutes before its geometrical sunrise and after its geometrical sunset.

The amount of refraction depends on atmospheric conditions, but it typically makes the Sun appear about 0.5 degrees higher than its true position on the horizon. This also contributes to the apparent flattening of the Sun’s disc when it is very low on the horizon.

112. The focal length of the objective lens of a telescope is 50 cm. If the

The focal length of the objective lens of a telescope is 50 cm. If the magnification of the telescope is 25, then the focal length of the eye-piece is

[amp_mcq option1=”12.5 cm” option2=”5 cm” option3=”2 cm” option4=”10 cm” correct=”option3″]

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The focal length of the eye-piece is 2 cm.

For a refracting telescope used in normal adjustment (final image at infinity), the angular magnification (M) is given by the ratio of the focal length of the objective lens (f_o) to the focal length of the eye-piece lens (f_e): M = f_o / f_e.
Given f_o = 50 cm and M = 25.
We can rearrange the formula to solve for f_e: f_e = f_o / M.
Substituting the given values: f_e = 50 cm / 25 = 2 cm.

A telescope achieves magnification by using an objective lens with a long focal length and an eye-piece lens with a short focal length. The objective forms a real, inverted image of a distant object at its focal plane, and the eye-piece acts as a magnifying glass to view this intermediate image.

113. The light energy escaping from the Sun can be spread by

The light energy escaping from the Sun can be spread by

[amp_mcq option1=”a shower of rain drops” option2=”a plane mirror” option3=”a convex lens” option4=”a combination of a convex lens and a concave lens” correct=”option1″]

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The correct answer is A) a shower of rain drops.

This question is likely referring to the phenomenon of dispersion of light, where white sunlight is separated into its constituent colors. A shower of raindrops acts like a large number of tiny prisms. As sunlight enters a raindrop, it is refracted, dispersed into its spectral colors, reflected internally, and then refracted again upon exiting the raindrop. This process creates a rainbow, which is a visible spectrum of sunlight. A plane mirror reflects light but does not disperse it. A convex lens converges light, and while it can refract light, its primary function is focusing, not spreading or dispersing white light into a spectrum like a prism or raindrop does. A combination of lenses can be used for various optical purposes but typically not for simply spreading or dispersing sunlight into its spectrum in the manner suggested by the formation of a rainbow.

Dispersion is the phenomenon where the speed of light in a medium depends on its wavelength (or color). Different wavelengths are refracted at slightly different angles, causing the separation of white light into its spectrum. Prisms and diffraction gratings are commonly used to demonstrate dispersion. A rainbow is a natural example of dispersion by water droplets.

114. Two convex lenses with power 2 dioptre are kept in contact with each o

Two convex lenses with power 2 dioptre are kept in contact with each other. The focal length of the combined lens system is

[amp_mcq option1=”0.10 m” option2=”2 m” option3=”4 m” option4=”0.25 m” correct=”option4″]

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UPSC NDA-1 – 2018

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When two thin lenses are kept in contact, the total power of the combination is the sum of the individual powers. The power of a lens (P) is given by the reciprocal of its focal length (f) in meters, i.e., P = 1/f.
Given the power of each lens is 2 Dioptre, the total power of the combined system is $P_{total} = P_1 + P_2 = 2 \, \text{D} + 2 \, \text{D} = 4 \, \text{D}$.
The focal length of the combined lens system (F) is the reciprocal of the total power: $F = 1 / P_{total} = 1 / 4 \, \text{D} = 0.25 \, \text{meters}$.

The power of lenses is additive when they are placed in contact. This property is useful for designing lens systems.

Dioptre (D) is the unit of power of a lens, defined as the reciprocal of the focal length in meters. A convex lens has positive power and focal length, while a concave lens has negative power and focal length.

115. Which one of the following statements about the refractive index of a

Which one of the following statements about the refractive index of a material medium with respect to air is correct ?

[amp_mcq option1=”It can be either positive or negative” option2=”It can have zero value” option3=”It is unity for all materials” option4=”It is always greater than one” correct=”option4″]

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UPSC NDA-1 – 2018

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The refractive index of a material medium ($n_m$) with respect to air ($n_{air}$) is defined as the ratio of the speed of light in air ($v_{air}$) to the speed of light in the medium ($v_m$). Since the speed of light in any material medium is always less than the speed of light in vacuum (and approximately less than the speed of light in air), the ratio $v_{air} / v_m$ will always be greater than 1 for any material medium (except vacuum or air itself, where the refractive index is 1).

Refractive index is a measure of how much the speed of light is reduced in a medium compared to air/vacuum. A higher refractive index indicates a slower speed of light in the medium and greater bending of light.

Refractive index values are typically positive. A refractive index of zero or negative would imply unusual optical properties, not characteristic of common materials. The refractive index of air with respect to vacuum is slightly greater than 1, but often approximated as 1. The refractive index of a medium with respect to vacuum is always greater than or equal to 1.

116. Which one of the following is the natural phenomenon based on which a

Which one of the following is the natural phenomenon based on which a simple periscope works ?

[amp_mcq option1=”Reflection of light” option2=”Refraction of light” option3=”Dispersion of light” option4=”Total internal reflection of light” correct=”option1″]

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UPSC NDA-1 – 2018

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A simple periscope uses two plane mirrors to change the direction of light rays. The mirrors are typically placed parallel to each other at an angle of 45 degrees to the main tube. Light rays from the object travel to the top mirror, are reflected downwards, travel through the tube, and are then reflected by the bottom mirror towards the observer’s eye. This bouncing of light rays off the mirrors is due to the phenomenon of reflection of light.

– A simple periscope allows observation of objects located above or below the observer’s direct line of sight.
– It utilizes plane mirrors placed at angles to redirect light.
– The change in direction of light upon hitting a mirror surface is called reflection.

More advanced periscopes, like those used in submarines, may also incorporate lenses and prisms (which use reflection or total internal reflection) to provide magnification, a wider field of view, and optical stability, but the fundamental principle in a simple periscope is reflection from plane mirrors.

117. The radii of curvature of the faces of a double convex lens are 10 cm

The radii of curvature of the faces of a double convex lens are 10 cm and 20 cm. The refractive index of the glass is 1.5. What is the power of this lens (in units of dioptre) ?

[amp_mcq option1=”+7·5 D” option2=”–7·5 D” option3=”+2·5 D” option4=”+5·0 D” correct=”option1″]

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UPSC NDA-1 – 2017

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The correct answer is +7.5 D.

For a thin lens, the power (P) is given by the reciprocal of the focal length (f) in meters, P = 1/f. The focal length of a lens in air can be calculated using the lensmaker’s formula: 1/f = (n – 1) * (1/R₁ – 1/R₂), where n is the refractive index of the lens material, and R₁ and R₂ are the radii of curvature of the two surfaces. For a double convex lens, assuming light comes from the left, the first surface is convex (R₁ > 0) and the second surface is also convex but faces the opposite direction (R₂ < 0).

Given: R₁ = +10 cm = +0.1 m, R₂ = -20 cm = -0.2 m (negative because the center of curvature is on the same side as the incoming light for the second surface of a double convex lens), and n = 1.5.
Using the lensmaker’s formula:
1/f = (1.5 – 1) * (1/0.1 – 1/(-0.2))
1/f = 0.5 * (1/0.1 + 1/0.2)
1/f = 0.5 * (10 + 5)
1/f = 0.5 * 15
1/f = 7.5 m⁻¹
Power P = 1/f = 7.5 Dioptre (D). Since the focal length is positive (1/7.5 m), it is a converging lens, which is expected for a double convex lens in air.

118. Which one of the following statements is correct about the magnificati

Which one of the following statements is correct about the magnification of an optical microscope?

[amp_mcq option1=”Magnification increases with the increase in focal length of eyepiece” option2=”Magnification increases with the increase in focal length of objective” option3=”Magnification does not depend upon the focal length of eyepiece” option4=”Magnification decreases with the increase in focal length of eyepiece” correct=”option4″]

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UPSC NDA-1 – 2017

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The correct statement is that magnification decreases with the increase in focal length of eyepiece. The total magnification of an optical microscope is the product of the magnification of the objective lens and the magnification of the eyepiece.

The magnification of the eyepiece (Me) is given by Me = D/fe (when the final image is formed at infinity) or Me = 1 + D/fe (when the final image is formed at the near point, D ≈ 25 cm). In both cases, Me is inversely proportional to the focal length of the eyepiece (fe). A larger fe results in a smaller Me. Similarly, the magnification of the objective lens (Mo) is approximately inversely proportional to its focal length (f₀). Mo ≈ L/f₀, where L is the tube length.

The total magnification M = Mo * Me. Therefore, increasing the focal length of the eyepiece (fe) decreases the eyepiece magnification (Me), which in turn decreases the total magnification of the microscope. Similarly, increasing the focal length of the objective (f₀) decreases the objective magnification (Mo), also decreasing the total magnification.

119. Match List I with List II and select the correct answer using the code

Match List I with List II and select the correct answer using the code given below the Lists:

List I (Disease)
A. Hypermetropia
B. Presbyopia
C. Myopia
D. Cataract

List II (Remedy)
1. Concave lens
2. Bifocal lens
3. Surgery
4. Convex lens

[amp_mcq option1=”A-4, B-2, C-1, D-3″ option2=”A-4, B-1, C-2, D-3″ option3=”A-3, B-1, C-2, D-4″ option4=”A-3, B-2, C-1, D-2″ correct=”option1″]

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UPSC NDA-1 – 2017

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This question requires matching common eye diseases/conditions with their standard remedies. Hypermetropia (farsightedness) is corrected with convex lenses. Presbyopia (age-related difficulty with near vision) is often managed with bifocal or progressive lenses. Myopia (nearsightedness) is corrected with concave lenses. Cataracts, which involve clouding of the eye’s lens, are primarily treated by surgical removal of the clouded lens and replacement with an artificial one. Thus, the correct matches are A-4, B-2, C-1, D-3.

Different refractive errors require specific types of corrective lenses based on how they affect the focusing of light on the retina. Cataracts are a structural issue requiring surgical intervention.

Concave lenses diverge light rays before they enter the eye (used for myopia). Convex lenses converge light rays (used for hypermetropia and presbyopia/reading). Bifocal lenses have different focal lengths in the upper and lower parts, typically for distance and near vision, respectively.

120. An optical illusion which occurs mainly in deserts during hot summer i

An optical illusion which occurs mainly in deserts during hot summer is based on the principle of

[amp_mcq option1=”Reflection” option2=”Interference” option3=”Dispersion” option4=”Total internal reflection” correct=”option4″]

This question was previously asked in

UPSC NDA-1 – 2017

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Optical illusions like mirages, which occur in hot deserts or over hot surfaces, are caused by the refraction and subsequent total internal reflection of light as it passes through layers of air with different temperatures and densities. The air near the hot ground is less dense and has a lower refractive index than the cooler air above. As light rays from the sky or distant objects travel downwards into the hotter, less dense layers, they bend upwards away from the normal. If the angle of incidence becomes greater than the critical angle, total internal reflection occurs, causing the light rays to be reflected upwards towards the observer’s eyes. The brain perceives these rays as coming from below, creating the illusion of a reflection, often resembling a pool of water.

– Mirages are caused by the bending of light (refraction) due to varying refractive indices in air layers of different temperatures.
– Total internal reflection occurs when light travels from a denser medium to a less dense medium at a sufficiently large angle of incidence.
– In hot conditions, air near the surface is hotter and less dense, creating conditions for total internal reflection of light traveling from cooler, denser air above.

Reflection is bouncing off a surface. Interference involves the superposition of waves. Dispersion is the splitting of light into its constituent colours based on wavelength. While refraction is the initial cause of bending, total internal reflection is crucial for the significant upward bending that creates the mirage image seen by the observer.