Wave Optics Test

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Wave Optics Test - 27

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Weekly Quiz Competition

Question 1
1 / -0

Who proposed wave nature of light ?

A
Huygen

B
Young

C
Fresnel

D
Maxwell

Solution

Huygens believed that light was made up of waves vibrating up and down perpendicular to the direction of the light travels. This is known as 'Huygens' Principle'. According to this theory, light waves are spherical, and these wave surfaces advance or spread out as they travel at the speed of light. This theory explains why light shining through a pin hole or slit will spread out rather than going in a straight line.
Question 2
1 / -0

The wavelength of $$\text{H}_a$$ line in hydrogen spectrum was found $$6563\ \text{A}^o$$ in the laboratory. If the wavelength of same line in the spectrum of a milky way is observed to be $$6586\ \text{A}^o $$ then the recessional velocity of the milky way will be

A
$$0.105 \times 10^6\ \text{ms}^{-1}$$

B
$$1.05 \times 10^6\ \text{ms}^{-1}$$

C
$$10.5\ \text{ms}^{-1}$$

D
$$\text{none of these}$$

Solution

According to the Doppler effect in light,
$$v=\dfrac{\Delta \lambda\times c}{\lambda}$$

$$ v= \dfrac{23.0 \times 10^{-10}\times 3.0 \times 10^8}{6563.0 \times 10^{-10}}$$

$$ v=1.051 \times 10^6\ \text{ms}^{-1}$$
Question 3
1 / -0

A star is receding away from earth with a velocity of $$10^5\ \text{ms}^{-1}.$$ If the wavelength of its spectral line is $$5700\ \text{A}^o $$ then Doppler shift will be

A
$$0.2\ \text{A}^o$$

B
$$1.9\ \text{A}^o $$

C
$$20\ \text{A}^o $$

D
$$200\ \text{A}^o $$

Solution

As,we know that Doppler effect in light$$,\ =\dfrac { \triangle \lambda }{ \lambda } =\dfrac { \triangle f }{ f } =\dfrac { v }{ c } $$

where, $$\triangle \lambda = \text{wavelength shift}$$

$$\triangle f = \text{frequency shift}$$

$$v= \text{speed of object}$$

$$c= \text{speed of light} = 3\times 10^8\ \text{m/s}$$

$$\dfrac { \triangle \lambda }{ \lambda } =\dfrac { v }{ c } \Rightarrow \triangle \lambda =\dfrac { \lambda v }{ c } $$

$$\triangle \lambda =\dfrac { 5700\times 10^5}{ 3 \times 10 ^ 8 } = 1.9 $$
Question 4
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Earth is moving towards a stationary star with a velocity $$100\ \text{kms}^{-1}$$. If the wavelength of light emitted by the star is $$5000\ \text{A}^o $$, then the apparent changes in wavelength observed by the observer on earth will be

A
$$0.67\ \text{A}^o $$

B
$$1.67\ \text{A}^o $$

C
$$16.7\ \text{A}^o $$

D
$$167\ \text{A}^o $$

Solution

According to the Doppler effect in light,

$$\Delta \lambda =\dfrac{v \lambda}{c} =\dfrac{10^5\times 5000\ \text{A}^o }{3\times 10^8} =1.67\ \text{A}^o$$

Option 'B' is correct.
Question 5
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The wavelength of light received from milky way is 0.4% higher than that from the same source on earth. The velocity of milky way with respect to earth will be

A
$$\displaystyle 0.2 \times 10^6 ms^{-1}$$

B
$$\displaystyle 1.2 \times 10^6 ms^{-1}$$

C
$$\displaystyle 2 \times 10^6 ms^{-1}$$

D
$$\displaystyle 5 \times 10^6 ms^{-1}$$

Solution

$$\Delta \lambda=\dfrac{v}{c} \lambda$$

$$v=\dfrac{ \Delta \lambda}{ \lambda} c$$

$$v=(\dfrac{ \Delta \lambda}{ \lambda}\times 100) \times (\dfrac{c}{100})=0.4 \times (\dfrac{3.0 \times 10^8}{100})=1.2\times 10^6 ms^{-1}$$
Question 6
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Dichorism means

A
selective absorption of unpolarised light.

B
selective absorption of dispersed light.

C
selective absorption of scattered light.

D
selective absorption of one of the polarised component.

Solution

Dichromism is the selective absorption of one orthogonal polarization component of an incident beam over the other. this phenomenon is due to anisotropy of the material, with one polarization component experiencing preferential absorption.
Question 7
1 / -0

The wave theory in its original form was first postulated by

A
Issac Newton

B
Thomas Young

C
Christian Huygens

D
Augustine Jean Fresnel

Solution

Christian Huygens postulated wave theory.
Question 8
1 / -0

Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil of diameter 3 mm. Approximately what is the maximum distance up to which these dots can be resolved by the eye.

A
5 m

B
6 m

C
1 m

D
4 m
Question 9
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A spectral line is obtained from a gas discharge tube at $$5000A^o $$ . If the rms velocity of gas molecules is $$10^5 ms^{-1}$$ then the width of spectral line will be

A
$$3.3 A^o $$

B
$$4.8 A^o $$

C
$$7.2 A^o $$

D
$$9.1A^o $$

Solution

$$\dfrac { \Delta \lambda }{ \lambda } =\dfrac { v }{ c } $$

we have to find 2x$$\Delta \lambda $$ (width of spectral line)

and we have been given that v = $$10^5$$m$$s^{-1}$$, $$\lambda=5000 A^o$$ and 'c' is speed of light so that gives us

$$\Delta \lambda = 5/3$$

and so width would be 10/3 = 3.3$$ A^o$$
Question 10
1 / -0

A rocket is receding away from earth with velocity $$0.2\text{c}.$$ The rocket emits signal of frequency $$4 \times 10^7\ \text{Hz}.$$ The apparent frequency of the signal produced by the rocket observed by the observer on earth will be

A
$$3\times 10^6\ \text{Hz}$$

B
$$4\times 10^6\ \text{Hz}$$

C
$$3.2\times 10^7\ \text{Hz}$$

D
$$5 \times 10^7\ \text{Hz}$$

Solution

According to the Doppler effect in light,

$$\dfrac{\delta \nu}{\nu}=\dfrac{v}{c}$$

$$\delta \nu=\dfrac{v}{c} \nu$$

$$\delta \nu=0.2 \times 4.0\times 10^7=0.8\times 10^7 s^{-1}$$

this will be a red shift,

therefore $$\nu'=(4.0-0.8)\times 10^7=3.2\times 10^7$$

Option "C" is correct.

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Wave Optics Test - 27

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Wave Optics Test - 27

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Question 1

Huygen

Young

Fresnel

Maxwell

Solution

Question 2

$$0.105 \times 10^6\ \text{ms}^{-1}$$

$$1.05 \times 10^6\ \text{ms}^{-1}$$

$$10.5\ \text{ms}^{-1}$$

$$\text{none of these}$$

Solution

Question 3

$$0.2\ \text{A}^o$$

$$1.9\ \text{A}^o $$

$$20\ \text{A}^o $$

$$200\ \text{A}^o $$

Solution

Question 4

$$0.67\ \text{A}^o $$

$$1.67\ \text{A}^o $$

$$16.7\ \text{A}^o $$

$$167\ \text{A}^o $$

Solution

Question 5

$$\displaystyle 0.2 \times 10^6 ms^{-1}$$

$$\displaystyle 1.2 \times 10^6 ms^{-1}$$

$$\displaystyle 2 \times 10^6 ms^{-1}$$

$$\displaystyle 5 \times 10^6 ms^{-1}$$

Solution

Question 6

selective absorption of unpolarised light.

selective absorption of dispersed light.

selective absorption of scattered light.

selective absorption of one of the polarised component.

Solution

Question 7

Issac Newton

Thomas Young

Christian Huygens

Augustine Jean Fresnel

Solution

Question 8

5 m

6 m

1 m

4 m

Question 9

$$3.3 A^o $$

$$4.8 A^o $$

$$7.2 A^o $$

$$9.1A^o $$

Solution

Question 10

$$3\times 10^6\ \text{Hz}$$

$$4\times 10^6\ \text{Hz}$$

$$3.2\times 10^7\ \text{Hz}$$

$$5 \times 10^7\ \text{Hz}$$

Solution

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