Wave Optics Test

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Wave Optics Test - 53

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Weekly Quiz Competition

Question 1
1 / -0

If light waves emitted by an ordinary source, for what period of time, the phase remains constant :-

A
$$10 sec$$

B
$$1 sec$$

C
$$10^{-3}$$ sec

D
$$10^{-8}$$ sec

Solution
Question 2
1 / -0

Angle of incidence is equal to the angle of reflection.

A
Always

B
Sometimes

C
Under special condition

D
Never

Solution

As per the low of reflection the angle of incident is always equal to angle
of reflection.
Hence option $$A$$ is correct answer.
Question 3
1 / -0

Two point source separated by $$d=5\mu m$$ emit light of wavelength $$\lambda=2\mu m$$ in phase. A circular wire of radius $$20\ mu m$$ is placed around the source as shown in figure.

A
Points $$A$$ and $$B$$ are dark and points $$C$$ and $$D$$ are bright.

B
Points $$A$$ and $$B$$ are bright and points $$C$$ and $$D$$ are dark.

C
Points $$A$$ and $$C$$ are dark and points $$B$$ and $$D$$ are bright.

D
Points $$A$$ and $$C$$ are bright and points $$B$$ and $$D$$ are dark.

Solution
Question 4
1 / -0

In the interference, two light waves are in the phase difference of at a point. If the yellow light is used, then the color of fringes at that point will be:-

A
Yellow

B
whitw

C
red

D
Black
Question 5
1 / -0

If ratio of amplitude of two interferring source is $$3:5$$. Then ratio of intensity of maxima and minima in interference pattern will be

A
$$25:16$$

B
$$5:3$$

C
$$16:1$$

D
$$25:9$$

Solution
Question 6
1 / -0

In YDSE, d = 2 mm, D = 2 m and$$\lambda $$ = 500 nm. If intensity of two slits are $$l _ { 0 }$$ and $$9 l _ { 0 }$$ then find intensity at $$y = \frac { 1 } { 6 }$$

A
$$7 l _ { 0 }$$

B
$$10 l _ { 0 }$$

C
$$16 l _ { 0 }$$

D
$$4 l _ { 0 }$$

Solution

Given$$:$$
$$d=2mm$$
$$D=2m$$
lambda$$=500nm$$
Intensities$$:$$ $${l_0}$$ and $$9{l_0}$$
path differences $$=xd/D$$
$$\frac{1}{6} \times {10^{ - 3}} \times 2 \times {10^{ - 3}}/2$$
$$ = 1.66 \times {10^{ - 7}}m$$
Phase difference$$ = \frac{{2\pi \Delta x}}{\lambda }$$
$$ = 2.08 = 0.664\pi = {119.52^0}$$
therefore$$,$$
$${I_{net}} = {l_0} + 9{l_0} + 2{\left( {9{l_0}} \right)^{1/2}}\cos \left( {119.52} \right)$$
$$ = 10{l_0} - 2.9{l_0}$$
$$ = 7.04{l_0} \approx 7{l_0}$$
Hence,
option $$(A)$$ is correct answer.
Question 7
1 / -0

What is the path difference of destructive interference :

A
$$n\lambda$$

B
$$n(\lambda +1)$$

C
$$\cfrac{(n+1)\lambda}{2}$$

D
$$\cfrac{(2n+1)\lambda}{2}$$

Solution

For destructive interference
Intensity should be minimum

$$I = I_1 + I_2 + 2 \sqrt{I_1 I_2} \cos \phi$$

$$\Rightarrow \cos \phi = -1 = \left(\dfrac{2n + 1}{2}\right) \pi = \phi$$

$$\Rightarrow \Delta x = \left(\dfrac{2n + 1}{2} \right) \lambda$$
Question 8
1 / -0

Statement-1 : In standard YDSE set up with visible light, the position on screen where phase difference is zero appears bright.
and
Statement-2 : In YDSE set up magnitude of electromagnetic field at central bright fringe is not varying with time.

A
Statement-1 is true statement-2 is true and statement-2 is correct explanation for statement-1.

B
Statement-1 is true statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

C
Statement-1 is true statement-2 is false.

D
Statement-1 is false statement-2 is true.

Solution

Electromagnetic field at a point depends also on time.
So statement-2 is false.
While Statement 1 is correct.
Question 9
1 / -0

In Y.D.S.E a film of a thickness of $$1.2\mu m$$ having $$2.5\mu m$$ is placed in the path of one slit & glass plate of $$1.5\mu m$$ is placed in front of other slits by which the central bright fringe do not shift, then the thickness of the glass is:-

A
$$3.6\mu m$$

B
$$3\mu m$$

C
$$1.2\mu m$$

D
$$2.4\mu m$$
Question 10
1 / -0

In a Young's double slit experiment D equals the distance of screen and d is the separation between the slit. The distance of the nearest point to the central maximum where the intensity is same as that due to a single slit, is equal to:-

A
$$\dfrac{D \lambda}{d}$$

B
$$\dfrac{D \lambda}{2d}$$

C
$$\dfrac{D \lambda}{3d}$$

D
$$\dfrac{2D \lambda}{d}$$

Solution

$$\textbf{Hint:}$$ Use the maximum Intensity formula.
$$\textbf{Step 1:}$$ let at distance y this happens$$.$$
$$ {I_0} = {I_0} + {I_0} + 2\sqrt {{I_0}} \sqrt {{I_0}} \cos \phi $$
$${I_0} = 2{I_0} + 2{I_0}\cos \phi $$
$$ 1 = 2\left[ {1 + \cos \phi } \right]$$
$$\dfrac{1}{2} = 1 + \cos \phi $$
$$\dfrac{{ - 1}}{2} = \cos \phi $$
$$\phi = \dfrac{{2\pi }}{3}$$
$$\textbf{Step 2:}$$ using phase difference formula,
$$ \dfrac{{2\pi }}{3} = \dfrac{{2\pi }}{\lambda }\left( {\Delta x} \right)$$
$$\Delta x\, = \dfrac{\lambda }{3}$$
$$\dfrac{{dy}}{D} = \dfrac{\lambda }{3}$$
$$y = \dfrac{{\lambda D}}{{3d}}$$
So,
$$\textbf{Option C is correct.}$$

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Re-Attempt Weekly Quiz Competition

Wave Optics Test - 53

Result

Wave Optics Test - 53

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SHARING IS CARING

Question 1

$$10 sec$$

$$1 sec$$

$$10^{-3}$$ sec

$$10^{-8}$$ sec

Solution

Question 2

Always

Sometimes

Under special condition

Never

Solution

Question 3

Points $$A$$ and $$B$$ are dark and points $$C$$ and $$D$$ are bright.

Points $$A$$ and $$B$$ are bright and points $$C$$ and $$D$$ are dark.

Points $$A$$ and $$C$$ are dark and points $$B$$ and $$D$$ are bright.

Points $$A$$ and $$C$$ are bright and points $$B$$ and $$D$$ are dark.

Solution

Question 4

Yellow

whitw

red

Black

Question 5

$$25:16$$

$$5:3$$

$$16:1$$

$$25:9$$

Solution

Question 6

$$7 l _ { 0 }$$

$$10 l _ { 0 }$$

$$16 l _ { 0 }$$

$$4 l _ { 0 }$$

Solution

Question 7

$$n\lambda$$

$$n(\lambda +1)$$

$$\cfrac{(n+1)\lambda}{2}$$

$$\cfrac{(2n+1)\lambda}{2}$$

Solution

Question 8

Statement-1 is true statement-2 is true and statement-2 is correct explanation for statement-1.

Statement-1 is true statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

Statement-1 is true statement-2 is false.

Statement-1 is false statement-2 is true.

Solution

Question 9

$$3.6\mu m$$

$$3\mu m$$

$$1.2\mu m$$

$$2.4\mu m$$

Question 10

$$\dfrac{D \lambda}{d}$$

$$\dfrac{D \lambda}{2d}$$

$$\dfrac{D \lambda}{3d}$$

$$\dfrac{2D \lambda}{d}$$

Solution

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