Optics

41. Which one of the following optical phenomena supports that the light i

Which one of the following optical phenomena supports that the light is a transverse wave ?

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Refraction
Diffraction
Interference
Polarization
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UPSC NDA-2 – 2023
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Polarization is an optical phenomenon that specifically demonstrates the transverse nature of light waves. Polarization occurs when the oscillations of the wave are restricted to a specific plane or direction perpendicular to the direction of propagation. Only transverse waves, where the oscillations are perpendicular to the direction of travel, can be polarized. Longitudinal waves, such as sound waves in air, oscillate parallel to the direction of propagation and cannot be polarized. Refraction, diffraction, and interference are phenomena that occur with both transverse and longitudinal waves.
– Polarization is the restriction of wave oscillations to a specific plane.
– Only transverse waves can be polarized.
– Refraction, diffraction, and interference occur for both wave types.
Polarization can happen through various methods like absorption (using polaroid filters), reflection (Brewster’s angle), scattering, and birefringence. The observation of polarization in light provided crucial evidence that light is a transverse wave.

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42. Ramesh cannot see distinctly objects kept beyond 2 m. This defect can

Ramesh cannot see distinctly objects kept beyond 2 m. This defect can be corrected by using a lens of power

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+ 0.5 D
- 0.5 D
+ 0.2 D
- 0.2 D
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B) – 0.5 D is the correct power of the lens required to correct the defect.
– The person cannot see objects distinctly beyond 2 m, meaning their far point is 2 m. This is a condition of myopia (nearsightedness).
– In myopia, distant objects (effectively at infinity) are focused in front of the retina.
– A diverging lens (concave lens) is used to correct myopia, as it diverges incoming light rays slightly before they reach the eye lens, causing them to focus further back on the retina.
– Concave lenses have negative power.
– The corrective lens should form a virtual image of an object at infinity (u = ∞) at the person’s far point (v = -2 m, as the image is virtual and on the same side as the object).
– Using the lens formula, 1/f = 1/v – 1/u:
– 1/f = 1/(-2) – 1/∞
– 1/f = -1/2 – 0
– 1/f = -1/2
– The power of the lens P is given by P = 1/f (in meters).
– P = 1/(-2 m) = -0.5 Diopters (D).
– Therefore, a concave lens of power -0.5 D is needed.

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43. Sita, 1·5 m high, stands before a plane mirror fixed on a wall to view

Sita, 1·5 m high, stands before a plane mirror fixed on a wall to view her full image. What should be the minimum height of the plane mirror so that Sita can view her image fully ?

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0·50 m
0·35 m
0·75 m
0·25 m
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UPSC NDA-2 – 2023
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The minimum height of the plane mirror required for a person to view their full image is half of the person’s height.
For a person of height H standing in front of a plane mirror, the minimum height of the mirror needed to see the entire image is H/2. This is because of the law of reflection; light rays from the top of the head and the bottom of the feet reflect off the mirror into the observer’s eyes. The reflection point for the feet is halfway between the feet and the eyes’ height, and similarly for the top of the head.
In this case, Sita’s height is 1.5 m. The minimum mirror height is 1.5 m / 2 = 0.75 m. The position of the mirror is also important; the bottom edge of the mirror should be at a height halfway between the person’s eyes and their feet.

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44. The streaming of light beams coming from the Sun through trees is said

The streaming of light beams coming from the Sun through trees is said to have suggested that light travels in straight line. The particles on the path of light beams are visible to us because

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dust particles in the air reflect light into our eyes
dust particles in the air scatter light into our eyes
dust particles in the air refract light into our eyes
dust particles in the air polarize light into our eyes
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The particles on the path of light beams coming from the Sun are visible to us because dust particles in the air scatter light into our eyes.
– In a perfectly clean atmosphere, a beam of light passing through it would be invisible from the side. We see light when it enters our eyes.
– When light encounters particles in the air, such as dust, smoke, or water droplets, it interacts with them.
– Scattering occurs when light waves are deflected in various directions by these particles.
– Some of the scattered light is directed towards our eyes, making the path of the light beam visible.
– This phenomenon is related to the Tyndall effect, which is the scattering of light by particles in a colloid or suspension.
Reflection typically occurs from surfaces, refraction is the bending of light as it passes from one medium to another, and polarization is the restriction of the direction of oscillation of light waves. While dust particles can reflect and refract light, scattering is the primary mechanism by which the path of a light beam through a dusty or smoky medium becomes visible.

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45. In which one of the following devices, the light energy is converted i

In which one of the following devices, the light energy is converted into the electrical energy?

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Light-emitting diode
Laser diode
Solar cell
Transistor
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The correct option is C, the Solar cell.
The question asks for a device where light energy is converted into electrical energy. This process is known as the photovoltaic effect.
– Light-emitting diode (LED) converts electrical energy into light energy.
– Laser diode also converts electrical energy into coherent light energy.
– Solar cell (photovoltaic cell) is specifically designed to absorb photons from sunlight and convert their energy into an electric current.
– Transistor is a semiconductor device used as an electronic switch or amplifier; it controls the flow of electrical current but does not primarily convert light energy to electrical energy (though some transistors can be light-sensitive, their main function isn’t energy conversion).
Therefore, the solar cell is the device that converts light energy into electrical energy.
Solar cells are the fundamental components of solar panels, which are widely used for generating renewable electricity. They are made of semiconductor materials, typically silicon, which release electrons when struck by photons of light, creating an electric current. This phenomenon is the basis of solar power generation.

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46. The refractive index of crown glass is close to 3/2. If the speed of l

The refractive index of crown glass is close to 3/2. If the speed of light in air is c, then the speed of light in the crown glass will be close to

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(3/2)c
(4/9)c
(2/3)c
(9/4)c
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The refractive index (n) of a medium is defined as the ratio of the speed of light in a vacuum (or approximately in air) to the speed of light in that medium (v). The formula is n = c / v, where c is the speed of light in vacuum/air.
Given that the refractive index of crown glass is close to 3/2, we have n = 3/2.
Using the formula n = c / v, we can rearrange it to solve for the speed of light in the glass (v): v = c / n.
Substituting the given refractive index: v = c / (3/2).
To divide by a fraction, we multiply by its reciprocal: v = c * (2/3) = (2/3)c.
The refractive index indicates how much the speed of light is reduced when it passes through a medium compared to its speed in a vacuum. A higher refractive index means a lower speed of light in the medium.
The speed of light is highest in a vacuum (approximately 3 x 10⁸ m/s) and slows down when it enters any medium, causing light to bend (refract). The refractive index is a dimensionless quantity.

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47. Two convex lenses have focal lengths of 50 cm and 25 cm, respectively.

Two convex lenses have focal lengths of 50 cm and 25 cm, respectively. If these two lenses are placed in contact, then the net power of this combination will be equal to

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+2 dioptre
+6 dioptre
-6 dioptre
+3 dioptre
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The power of a lens (P) is the reciprocal of its focal length (f) in meters (P = 1/f). For a combination of thin lenses in contact, the total power (P_net) is the sum of the individual powers (P_net = P1 + P2 + …).
Given focal lengths: f1 = 50 cm = 0.5 m and f2 = 25 cm = 0.25 m. Both are convex lenses, so focal lengths are positive.
Power of the first lens: P1 = 1 / f1 = 1 / 0.5 m = +2 Dioptre (D).
Power of the second lens: P2 = 1 / f2 = 1 / 0.25 m = +4 Dioptre (D).
Net power of the combination: P_net = P1 + P2 = +2 D + +4 D = +6 D.
The power of a lens is a measure of its ability to converge or diverge light, and for lenses in contact, powers are additive.
The unit of power is the Dioptre (D), defined as the reciprocal of the focal length in meters. Convex lenses have positive power (converging), and concave lenses have negative power (diverging).

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48. Which one of the following wavelengths corresponds to the wavelength o

Which one of the following wavelengths corresponds to the wavelength of X-rays?

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500 nm
5000 nm
100 nm
1 nm
This question was previously asked in
UPSC NDA-2 – 2022
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Electromagnetic radiation is classified by wavelength or frequency. The electromagnetic spectrum includes (in order of decreasing wavelength): Radio waves, Microwaves, Infrared radiation, Visible light, Ultraviolet radiation, X-rays, and Gamma rays.
Visible light wavelengths are typically in the range of 400 nm to 700 nm.
Ultraviolet (UV) radiation has wavelengths shorter than visible light, usually in the range of 10 nm to 400 nm.
X-rays have even shorter wavelengths, generally ranging from about 0.01 nm to 10 nm.
Gamma rays have the shortest wavelengths, typically less than 0.1 nm.
Comparing the given options to the typical range of X-ray wavelengths (0.01 nm – 10 nm):
A) 500 nm falls in the visible light spectrum.
B) 5000 nm (5 µm) falls in the infrared spectrum.
C) 100 nm falls in the ultraviolet spectrum.
D) 1 nm falls within the typical range of X-ray wavelengths.
X-rays are high-energy photons commonly used in medical imaging (radiography, CT scans) and material analysis (X-ray crystallography, fluorescence). They are produced when high-speed electrons strike a metal target or by electron transitions in atoms.

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49. The image of an object formed by a plane mirror is

The image of an object formed by a plane mirror is

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erect, real and larger.
erect, virtual and same size.
inverted, virtual and same size.
inverted, real and smaller.
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UPSC NDA-2 – 2021
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The image of an object formed by a plane mirror is erect, virtual and the same size as the object.
A plane mirror forms an image that is always virtual (cannot be projected onto a screen), erect (same orientation as the object), laterally inverted (left appears right and vice versa), and of the same size as the object. The image is also located as far behind the mirror as the object is in front.
Real images are formed when light rays converge at a point after reflection or refraction, whereas virtual images are formed when light rays appear to diverge from a point. Plane mirrors produce virtual images because the reflected rays do not actually meet but only appear to meet behind the mirror.

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50. When a light beam falls on a triangular glass prism, a band of colours

When a light beam falls on a triangular glass prism, a band of colours is obtained. Which one of the following statements is correct in this regard?

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Red light bends the most, as the refractive index of glass for red light is greatest.
Red light bends the most, as the refractive index of glass for red light is lowest.
Violet light bends the most, as the refractive index of glass for violet light is greatest.
Violet light bends the most, as the refractive index of glass for violet light is lowest.
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UPSC NDA-2 – 2021
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The correct answer is that Violet light bends the most because the refractive index of glass for violet light is greatest.
When white light passes through a prism, it splits into its constituent colours due to dispersion. The amount of bending (deviation) of light by a prism depends on the refractive index of the prism material for that specific colour. According to Cauchy’s formula and experimental observations, the refractive index of a material decreases as the wavelength of light increases. Violet light has the shortest wavelength among the visible colours, while red light has the longest wavelength. Therefore, the refractive index of glass is highest for violet light and lowest for red light. A higher refractive index leads to a greater deviation (bending).
The deviation of light by a prism is given approximately by $\delta = (\mu – 1)A$, where $\mu$ is the refractive index of the prism material and A is the angle of the prism. Since $\mu_{\text{violet}} > \mu_{\text{red}}$, it follows that $\delta_{\text{violet}} > \delta_{\text{red}}$. This causes violet light to be deviated the most and red light the least, resulting in the separation of colours observed as a spectrum.

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