Wave Optics Test

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Wave Optics Test - 66

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Weekly Quiz Competition

Question 1
1 / -0

Off in the distance, you see the headlights of a car, but they are indistinguishable from the single headlight of a motorcycle. Assume the car's headlights are now switched from low beam to high beam so that the light intensity you receive becomes three times greater. What then happens to your ability to resolve the two light sources?

A
It increases by a factor of $$ 9 . $$

B
It increases by a factor of $$ 3 . $$

C
It remains the same.

D
It becomes one-third as good.

E
It becomes one-ninth as good.

Solution

The ability to resolve light sources depends on diffraction, not on intensity.
Question 2
1 / -0

Suppose Young's double-slit experiment is performed in air using red light and then the apparatus is immersed in water. What happens to the interference pattern on the screen?

A
It disappears

B
The bright and dark fringes stay in the same locations, but the contrast is reduced.

C
The bright fringes are closer together.

D
The bright fringes are farther apart.

Solution

Underwater, the wavelength of the light decreases according to $$\lambda_{water} = \lambda_{air}/\eta_{water}.$$ Since the angles between positions of light and dark bands, being small, are approximately proportional to $$\lambda,$$ the underwater fringe separation decrease.
Question 3
1 / -0

A wedge containing two glass plates touching at one end and separated at the other end by the wire of diameter $$48\times 10^{-6}m$$ is illuminated normally by light of wavelength $$\lambda $$ = 6400 $$\mathring{A}$$. The length of the wedge $$l $$ is $$12 cm.$$ How many bright images can be seen over this $$12 cm $$ distance?

A
$$100$$

B
$$150$$

C
$$120$$

D
$$90$$

Solution

We have path difference $$= 2d = (2n +1) \dfrac {\lambda}{2}$$,
where $$d$$ is the gap of air at any point along the length of glass plate
$$\implies d = ( n+\dfrac{1}{2}) \dfrac{\lambda}{2}$$
$$\implies n \approx \dfrac{2d}{ \lambda }= \dfrac{2 \times 48 \times 10^{-6}}{6400 \times 10^{-10}}=150$$
Question 4
1 / -0

Directions For Questions

In the Young's double slit experiment a point source of $$\lambda = 5000 \mathring{A} $$ is placed slightly off the central axis as shown in the figure.

...view full instructions

Find the nature and order of the interference at the point P :

A
$$70^{th}$$ maxima

B
$$80^{th}$$ minima

C
$$60^{th}$$ maxima

D
$$70^{th}$$ minima

Solution

The optical path difference ($$\Delta x$$) between the waves at $$P$$ is given by
$$\Delta x = S_2P - S_1P = {\dfrac {y_1 d}{D_1}} + {\dfrac {y_1 d}{D_1}}$$
$$\Delta x = \dfrac {(1)(10)}{10^3} + \dfrac {(5)(10)}{2 \times 10^3}$$
Therefore, $$\Delta x = 0.035 mm$$
Also, $$ \Delta x = n \lambda = 0.035 mm$$
$$\implies n = \dfrac {0.035 \times 10^{-3}} {5000 \times 10^{-10}} = 70$$
Hence a maxima of $$70^{th}$$ order is obtained at P.
Question 5
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Directions For Questions

In the Young's double slit experiment a point source of $$\lambda = 5000 \mathring{A} $$ is placed slightly off the central axis as shown in the figure.

...view full instructions

Find the nature and order of the interference at O

A
$$20^{th} $$ minima

B
$$20^{th} $$ maxima

C
$$10^{th} $$ maxima

D
$$10^{th} $$minima

Solution

The optical path difference ($$\Delta x$$) between the waves at $$P$$ is given by
$$\Delta x = S_2P - S_1P = {\dfrac {y d}{D}}$$
Therefore, $$\Delta x = 0.01 mm$$
Also, $$ \Delta x = n \lambda = 0.01 mm$$
$$\implies n = \dfrac {0.01 \times 10^{-3}} {5000 \times 10^{-10}} = 20$$
Hence a maxima of $$20^{th}$$ order is obtained at 0.
Question 6
1 / -0

Directions For Questions

A concave mirror of radius of curvature $$10 cm$$ is cut into two equal parts and placed in front of a monochromatic light source of wavelength $$2000$$$$A^o$$ as shown in the figure. Consider only interference in reflected light after first reflection from mirrors.

...view full instructions

If half of reflecting surface of upper part of mirror is painted black, choose correct options from the following

A
Intensity of maxima and minima will increase

B
Intensity at minima will increase and at maxima, intensity will decrease

C
Intensity at minima will remain zero and at maxima, intensity will decrease

D
Intensity at maxima remains unchanged but at minima, intensity will increase

Solution

As half reflecting surface of one part is painted black then intensity of one source will decrease so intensity at maxima will decrease and at minima it will increase (when intensity of both sources is same then there is zero intensity at minima).
Question 7
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Directions For Questions

A concave mirror of radius of curvature $$10 cm$$ is cut into two equal parts and placed in front of a monochromatic light source of wavelength $$2000$$$$A^o$$ as shown in the figure. Consider only interference in reflected light after first reflection from mirrors.

...view full instructions

If the point object is moved away from mirror normal to screen then ,

A
fringe width will increase

B
fringe width will decrease

C
fringe width will first increase then decrease

D
Remain unchanged

Solution

As source is moved away from the mirror both images will move towards the mirrors.
'D' will increase and 'd' will decrease.
Question 8
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Directions For Questions

Figure illustrates the interference experiment with Fresnel mirror. The angle between the mirrors $$a=12'$$. The distances from the mirrors intersection line to the narrow slit $$S$$ and the screen $$E$$ is equal to $$r=10cm$$ and $$b=130cm$$ respectively. The monochromatic wavelength of light $$\lambda=550nm$$.

...view full instructions

Find fringe width and number of possible maxima on the screen $$E$$:

A
$$1.1mm, 8$$

B
$$1.1mm, 9$$

C
$$0.8mm,8$$

D
$$0.9mm,9$$

Solution

$$ D=b+r=1.4m$$
$$ d={ S }_{ 1 }{ S }_{ 2 }=2r\delta =\dfrac { 2\times 0.1\times 1 }{ 5\times 57 } rad$$
$$\beta =\dfrac { \lambda D }{ d } =\dfrac { 550\times { 10 }^{ -9 }\times 1.4\times 5\times 57 }{ 2\times 0.1\times 1 } =1.1mm$$
Number of possible maxima $$ =\dfrac { 2b\alpha }{ \beta } =\dfrac { 2\times 1.3\times 0.2 }{ 1.1\times { 10 }^{ -3 }\times 5\times 57 } =8.3$$
$$n=8.3+1\approx 9$$
Question 9
1 / -0

The shape of the nodal curves is

A
Elliptical

B
Parabolic

C
Hyperbolic

D
Circular
Question 10
1 / -0

Light of wavelength $$500nm$$ goes through a pinhole of $$0.2mm$$ and falls on a wall at a distance of $$2m$$. What is the radius of the central bright spot formed on the wall?

A
$$2.37 cm$$

B
$$1.37 cm$$

C
$$3.37 cm$$

D
$$7.37 cm$$

Solution

$$R=\displaystyle\frac{1.22\lambda D}{r}$$ $$=\displaystyle\frac{1.22\times 560\times 2\times 10^{-9}}{0.1\times 10^{-9}}$$
$$=1.37cm$$

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Wave Optics Test - 66

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Wave Optics Test - 66

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Question 1

It increases by a factor of $$ 9 . $$

It increases by a factor of $$ 3 . $$

It remains the same.

It becomes one-third as good.

It becomes one-ninth as good.

Solution

Question 2

It disappears

The bright and dark fringes stay in the same locations, but the contrast is reduced.

The bright fringes are closer together.

The bright fringes are farther apart.

Solution

Question 3

$$100$$

$$150$$

$$120$$

$$90$$

Solution

Question 4

$$70^{th}$$ maxima

$$80^{th}$$ minima

$$60^{th}$$ maxima

$$70^{th}$$ minima

Solution

Question 5

$$20^{th} $$ minima

$$20^{th} $$ maxima

$$10^{th} $$ maxima

$$10^{th} $$minima

Solution

Question 6

Intensity of maxima and minima will increase

Intensity at minima will increase and at maxima, intensity will decrease

Intensity at minima will remain zero and at maxima, intensity will decrease

Intensity at maxima remains unchanged but at minima, intensity will increase

Solution

Question 7

fringe width will increase

fringe width will decrease

fringe width will first increase then decrease

Remain unchanged

Solution

Question 8

$$1.1mm, 8$$

$$1.1mm, 9$$

$$0.8mm,8$$

$$0.9mm,9$$

Solution

Question 9

Elliptical

Parabolic

Hyperbolic

Circular

Question 10

$$2.37 cm$$

$$1.37 cm$$

$$3.37 cm$$

$$7.37 cm$$

Solution

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