Wave Optics Test

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Wave Optics Test - 74

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Weekly Quiz Competition

Question 1
1 / -0

In a Youngs double-slit experiment, let $$\beta$$ be the fringe width, and let $${l}_{0}$$ be the intensity at the central bright fringe. At a distance $$x$$ from the central bright fringe, the intensity will be:

A
$${ l }_{ 0 }\cos { \left( \dfrac { x }{ \beta } \right) }$$

B
$${ l }_{ 0 }\cos ^{ 2 }{ \left( \dfrac { x }{ \beta } \right) }$$

C
$${ l }_{ 0 }\cos ^{ 2 }{ \left( \dfrac { \pi x }{ \beta } \right) }$$

D
$$\dfrac { { l }_{ 0 } }{ 4 } \cos ^{ 2 }{ \left( \dfrac { \pi x }{ \beta } \right) }$$

Solution

$$\Delta =X\left( d/D \right)$$
$$\therefore\quad$$ phase difference$$=\phi=\dfrac {2\pi}{\lambda}\Delta $$
Let $$a=$$ amplitude at the screen due to each slit
$$\therefore\quad {l}_{0}=k{(2a)}^{2}={4ka}^{2}$$, where $$k$$ is constant.
For phase difference $$\phi$$, amplitude $$=A=2a \cos(\phi/2)$$.
Intensity, $$l={ kA }^{ 2 }=k\left( { 4a }^{ 2 } \right) \cos ^{ 2 }{ \left( \phi /2 \right) } { l }_{ 0 }\cos ^{ 2 }{ \left( \pi \Delta /\lambda \right) }$$
$$={ l }_{ 0 }\cos ^{ 2 }{ \left( \dfrac { \pi }{ \lambda } .\dfrac { xd }{ D } \right) } ={ l }_{ 0 }\cos ^{ 2 }{ \left( \dfrac { \pi x }{ \beta } \right) }.$$
Hence $$(C)$$ is correct.
Question 2
1 / -0

In Young's double slit experiment, the slits are $$2$$ mm apart and are illuminated by photons of two wavelengths $$\lambda_1=12000\overset{o}{A}$$ and $$\lambda_2=10000\overset{o}{A}$$. At what minimum distance from the common central bright fringe on the screen $$2$$ m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?

A
$$3$$ mm

B
$$8$$ mm

C
$$6$$ mm

D
$$4$$ mm

Solution

$$\dfrac { { \lambda }_{ 1 } }{ { \lambda }_{ 2 } } =\dfrac { { h }_{ 1 } }{ { h }_{ 2 } } $$

$$=\dfrac { 12000 }{ 10000 } =\dfrac { 6 }{ 5 } $$

$$=\dfrac { { u }_{ 1 }{ \lambda }_{ 1 }D }{ d } =\dfrac { 5\times 12000\times { 10 }^{ -10 }\times 2 }{ 2\times { 10 }^{ -3 } } $$

$$=5\times 1.2\times { 10 }^{ 4 }\times { 10 }^{ -10 }\times { 10 }^{ 3 }=6mm$$
Question 3
1 / -0

A source and a listener arc moving towards each other with a speed $$(1/10)th$$ that of sound. If frequency of sound emitted by the source is $$f$$ than the frequency heard by listener will be

A
$$f$$

B
$$1.11\ f$$

C
$$1.22\ f$$

D
$$1.27\ f$$

Solution
Question 4
1 / -0

In $$YDSE$$, the central bright fringes is at mid-point of screen. On both side of mid-point fringes are obtained. Number of fringes on either side is $$n_1$$, with air between slits and screen. When water $$^a\mu_{W}=\dfrac {4}{3}$$ is filled $$'n_2'$$, number of fringes are obtained on either side, then $$n_{2}$$ is

A
$$\dfrac {8n_{1}-1}{6}$$

B
$$\dfrac {7n_{1}-1}{6}$$

C
$$\dfrac {8n_{1}+1}{6}$$

D
$$\dfrac {9n_{1}-1}{6}$$

Solution
Question 5
1 / -0

Two coherent sources of wavelengths $$4.8\times {10}^{-7}m$$ produce a steady interference pattern
The path difference corresponding to $$10th$$ order maximum will be

A
$$12\times {10}^{-6}m$$

B
$$4.8\times {10}^{-8}m$$

C
$$24\times {10}^{-7}m$$

D
$$4.8\times {10}^{-6}m$$

Solution
Question 6
1 / -0

In a YDSE experiment if a slab whose refractive index can be varied is placed in front of one of the slits then the variation of resultant intensity at mid-point of screen with $$\mu(\mu\ge 1)$$ will be best represented by (assume slits of equal width and there is not absorption by slab)

A

B

C

D

Solution
Question 7
1 / -0

In a Young's double slit experiment , a slab of thickness $$1.2 \mu m$$ and refractive index $$1.5$$ is placed in front of one slit and another slab of thickness t and refractive index $$2.5$$ is placed in front of the second slit. If the position of the central fringe remains unaltered, then the thickness is

A
$$0.4 \mu m$$

B
$$0.8 \mu m$$

C
$$1.2 \mu m$$

D
$$0.72 \mu m$$

Solution
Question 8
1 / -0

A source of sound emitting a note of frequency $$500\ Hz$$ moves towards an observer with a velocity $$v$$ equal to half the velocity of sound. If the observer moves away from the source with the same velocity, then the apparent frequency heard by the observer is

A
$$250\ Hz$$

B
$$500\ Hz$$

C
$$750\ Hz$$

D
$$1500\ Hz$$

Solution
Question 9
1 / -0

Consider that the screen starts moving towards right with speed $$v$$. At $$t=0$$, second maxima was lying at point $$P$$. At what time $$t$$, first minima will be lying at the point $$P$$?

A
$$\dfrac {D}{v}$$

B
$$\dfrac {2D}{v}$$

C
$$\dfrac {3D}{v}$$

D
$$\dfrac {4D}{v}$$

Solution
Question 10
1 / -0

A source of sound of frequency $$258\ Hz$$ is moving rapidly towards a wall with a velocity of $$5m/s$$. How many beats per second will be heard by the observer situated on the source itself if sound travels at a speed of $$330\ m/s$$

A
$$6$$

B
$$8$$

C
$$10$$

D
$$4$$

Solution