Wave Optics Test

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Wave Optics Test - 50

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Weekly Quiz Competition

Question 1
1 / -0

The waves are observed by a child sitting in a rowboat off shore. Which of the following properties of the waves seen by the child would be greater when the boat is moving away from the beach than the boat is stationary with respect to the beach?
I. Speed of the waves with respect to the boat.
II. Frequency at which the boat encounters successive wave crests.
III. Distance between adjacent wave crests

A
I only

B
III only

C
I and II only

D
II and III only

E
I, II, and III

Solution

If child is moving away from the shore then it will absorved low wavelength higher frequency and High speed also with respect to child and vice versa.
Hence correct option is C.
Question 2
1 / -0

In which of the following cases do we obtain a plane wave front?

A
Light emitted by a point source in an isotropic medium

B
Light emerging from a convex lens when a point source is placed at its focus

C
Light of the sun reaching the earth

D
Light diverging from a slit.

Solution

Isotropic medium is medium which doesn't depend on direction of light.
In this medium speed of light is constant and wave travel from source to infinity than it make plane wave front.
In option A given light emitted by the point source in an isotropic medium that means direction of light is constant and it can travel for a long distance. If light will travel for long distance than it will form plane wave front.
Hence,
correct option is A.
Question 3
1 / -0

How does the fringe width in a double slit interference pattern change, when the distance between the slits is increased ?

A
Slit width decreases

B
Slit width increases

C
no effect

D
Slits disappears

Solution

We know that fringe width is equal to wavelength multiplied by distance from screen to slit divided by separation of two slit
$$\beta =\frac { \lambda D }{ d } $$
Here,
Fring width is inversely proportional to slit separation therefore, When fring width will increase than slit separation will decease.
Correct option is A.
Question 4
1 / -0

In a double slit experiment $$ D=1m,d=0 .2cm$$ and$$\lambda={ 6000 }\mathring { A }$$. The distance of the point from the central maximum where intensity is $$75\%$$ of the at the centre will be:

A
$$0.01\ mm$$

B
$$0.03\ mm$$

C
$$0.05\ mm$$

D
$$0.1\ mm$$

Solution

Given,
Distance between slit and screen is $$D=1m$$
Slit width is $$d=0.2cm=0.2\times { 10 }^{ -2 }m$$
Wavelength of light is $$\lambda =6000{ A }^{ 0 }=6000\times { 10 }^{ -7 }m$$
$$\frac { I }{ { I }_{ 0 } } =\frac { 75 }{ 100 } =\frac { 3 }{ 4 } $$
Intensity of light in the fringe pattern is
$$I={ I }_{ 0 }{ cos }^{ 2 }\left( \frac { \theta }{ 2 } \right) $$
By equating
$$\frac { 3 }{ 4 } { I }_{ 0 }={ I }_{ 0 }{ cos }^{ 2 }\left( \frac { \theta }{ 2 } \right) \\ \frac { \theta }{ 2 } =\frac { \pi }{ 12 } \\ \theta =\frac { \pi }{ 6 } $$
Let $$\triangle \theta $$ is path difference
$$\frac { \pi }{ 6 } =\frac { \pi yd }{ \lambda D } \\ y=\frac { \lambda D }{ 6d } $$
Substitute all value in above equation
$$y=\frac { 6000\times { 10 }^{ -7 }\times 1 }{ 6\times 0.2\times { 10 }^{ -2 } } \\ \quad =0.05mm$$
correct option is C.
Question 5
1 / -0

In Young's double slit experiment, $$5^{th}$$ dark fringe is formed opposite to one of the slits. If $$D$$ is the distance between slits and the screen, and $$d$$ is the separation between the slits, then the wavelength of light used is ?

A
$$\dfrac {d^{2}}{6D}$$

B
$$\dfrac {d^{2}}{5D}$$

C
$$\dfrac {d^{2}}{15D}$$

D
$$\dfrac {d^{2}}{9D}$$

Solution

Correct option is D
Question 6
1 / -0

Which of the following is incorrect?

A
A thin convex lens of focal length $${f}_{1}$$ is placed in contact with a thin concave lens of focal length $${f}_{2}$$. The combination will act as convex lens if $${f}_{1}<{f}_{2}$$

B
Light on reflection at water-glass boundary will undergo a phase change of $$\pi$$

C
Spherical aberration is minimized by achromatic lens

D
If the image of distant object is formed in front of the retina then defect of vision may be myopia

Solution
Question 7
1 / -0

The two coherent sources of equal intensity produce maximum intensity of $$100$$ units at a point. If the intensity of one of the sources is reduced by $$50\%$$ by reducing its width then the intensity of light at the same point will be

A
90

B
81

C
67

D
72.85

Solution

Hint: The resultant intensity of sources can be written as,
$$I_{ R }={ I }_{ 1 }+{ I }_{ 2 }+2\sqrt { { I }_{ 1 }{ I }_{ 2 } } $$

Step 1: Given data
Maximum intensity $${ I }_{ 0 }=100units$$
Intensity of one source is reduced by $$50 percent$$
We know that when two source having intensity of $$I_{ 1 }\quad and\quad { I }_{ 2 }$$ Then resultant intensity is
$$I_{ R }={ I }_{ 1 }+{ I }_{ 2 }+2\sqrt { { I }_{ 1 }{ I }_{ 2 } } $$
Here,
$${ I }_{ 1 }={ I }_{ 0 }\\ { I }_{ 2 }={ I }_{ 0 } $$
Putting all value in above equation
$$I_{ R }={ I }_{ 0 }+ { I }_{ 0 } +2\sqrt { { I }_{ 0 }\times { I }_{ 0 } } \\ \quad ={ I }_{ 0 }(1+1 +2 )\\ $$
$${ I }_{ 0 }=\frac { { I }_{ R } }{ 4 } =\frac { 100 }{ 4 } =25$$

Step 2: Find the resultant intensity.
When one source is reduced
$${ I }_{ 1 }={ I }_{ 0 }\\ { I }_{ 2 }={ I }_{ 0 }-{ I }_{ 0 }\times \frac { 50 }{ 100 } =\frac { { I }_{ 0 } }{ 2 } $$
Putting all value in above equation
$$I_{ R }={ I }_{ 0 }+\frac { { I }_{ 0 } }{ 2 } +2\sqrt { { I }_{ 0 }\times \frac { { I }_{ 0 } }{ 2 } } \\ \quad ={ I }_{ 0 }(1+\frac { 1 }{ 2 } +\sqrt { 2 } )\\ \quad =25\times 2.91\\ \quad =72.85$$
Correct option is D.
Question 8
1 / -0

The speed of the light in the medium is :-

A
maximum on the axis of the beam

B
minimum on the axis of the beam

C
the same everywhere in the beam

D
directly proportional to the intensity I

Solution
Question 9
1 / -0

Monochromatic green light of wavelength $$5\times10^{-7}m$$ illuminates a pair of slits 1 mm apart. The separation of bright lines on the interference pattern formed on a screen 2 m away is

A
1.0 mm

B
1.5 mm

C
2.0 mm

D
1.9 mm

Solution

We know that for Young's Double Slit Experiment
$$\beta=\cfrac{\lambda D}{d}$$
Here,
$$\lambda=5\times10^{-7}m^{-1}\\D=2m\\d=10^{-3}m$$
Now, $$\beta=\cfrac{5\times10^{-7}\times2}{10^{-3}}m=10^{-3}=1.0mm$$
Thus $$\beta=1.0mm$$
Question 10
1 / -0

Two superimposing waves are represented by equation $${y}_{1}=2\sin { 2\pi } \left( 10t-0.4x \right)$$ and $${y}_{2}=4\sin { 2\pi } \left( 20t-0.8x \right)$$. The ratio of $${I}_{max}$$ to $${I}_{min}$$ is

A
$$36:4$$

B
$$25:9$$

C
$$1:4$$

D
$$4:1$$

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Wave Optics Test - 50

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Wave Optics Test - 50

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Question 1

I only

III only

I and II only

II and III only

I, II, and III

Solution

Question 2

Light emitted by a point source in an isotropic medium

Light emerging from a convex lens when a point source is placed at its focus

Light of the sun reaching the earth

Light diverging from a slit.

Solution

Question 3

Slit width decreases

Slit width increases

no effect

Slits disappears

Solution

Question 4

$$0.01\ mm$$

$$0.03\ mm$$

$$0.05\ mm$$

$$0.1\ mm$$

Solution

Question 5

$$\dfrac {d^{2}}{6D}$$

$$\dfrac {d^{2}}{5D}$$

$$\dfrac {d^{2}}{15D}$$

$$\dfrac {d^{2}}{9D}$$

Solution

Question 6

A thin convex lens of focal length $${f}_{1}$$ is placed in contact with a thin concave lens of focal length $${f}_{2}$$. The combination will act as convex lens if $${f}_{1}<{f}_{2}$$

Light on reflection at water-glass boundary will undergo a phase change of $$\pi$$

Spherical aberration is minimized by achromatic lens

If the image of distant object is formed in front of the retina then defect of vision may be myopia

Solution

Question 7

90

81

67

72.85

Solution

Question 8

maximum on the axis of the beam

minimum on the axis of the beam

the same everywhere in the beam

directly proportional to the intensity I

Solution

Question 9

1.0 mm

1.5 mm

2.0 mm

1.9 mm

Solution

Question 10

$$36:4$$

$$25:9$$

$$1:4$$

$$4:1$$

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