Wave Optics Test

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Wave Optics Test - 60

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following quantities is not carried by light ?

A
Angular momentum

B
Linear momentum

C
Energy

D
None of the above

Solution
Question 2
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The equation of a transverse wave is $$z=a\ \sin \left\{\omega t-\dfrac {k}{2}(x+y)\right\}$$
The equation of wavefront is :

A
$$x=$$ constant

B
$$y=$$ constant

C
$$x+y=$$ constant

D
$$y-x=$$ constant

Solution
Question 3
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An isotropic point source emits light. A screen is situated at a given distance. If the distance between sources and screen is decreased by $$2\%$$, illuminance will increase by:

A
$$1\%$$

B
$$2\%$$

C
$$3\%$$

D
$$4\%$$

Solution

For isotropic point source
$$E\propto\dfrac{1}{r^{2}}$$

For small change, $$\dfrac{\Delta E}{\Delta r}=\dfrac{-2k }{r^{3}}$$

$$\dfrac{\Delta E}{\Delta r}=-2\dfrac{k}{r^{2}}\dfrac{1}{r}$$ or $$\dfrac{\Delta E}{\Delta r}=-2\dfrac{E}{r}$$

or $$\dfrac{\Delta E}{I}=2\left(-\dfrac{\Delta r}{r}\right)\therefore \% \Delta E=2\times 2\%=4\%$$

Hence, (d) is correct.
Question 4
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Two sources $$S_{1}$$ and $$S_{2}$$ separated by $$2$$ metres vibrate according to the equations $$y_{1} = 0.03\sin \pi t$$ and $$y_{2} = 0.02 \sin \pi t$$ where $$y_{1}$$ and $$y_{2}$$ are in metres. They send out waves of velocity $$1.5 m/s$$. The amplitude of the resultant motion of particle collinear with $$S_{1}$$ and $$S_{2}$$ and at the middle of $$S_{1} S_{2}$$ will be :

A
$$0.05\ m$$

B
$$0.01\ m$$

C
$$0.11\ m$$

D
$$0.06\ m$$

Solution
Question 5
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If $$n$$ coherent sources of intensity $$I_0$$ are super imposed at a point, the intensity of the point is :

A
$$nI_0$$

B
$$n^2I_0$$

C
$$n^3I_0$$

D
$$\dfrac{I_0}{n}$$

Solution
Question 6
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The wavefronts of a light coming from a distant source of unknown shape are nearly

A
plane

B
elliptical

C
cylindrical

D
spherical

Solution

When the point source or linear source of light is at very large distance, a small portion of spherical or cylindrical wavefront appears to be plane. Such a wavefront is plane wavefront.
hence option A is correct.
Question 7
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In YDSE, find the thickness of a glass slab $$(\mu=1.5)$$ which should be placed before the upper slit $$S_{1}$$ so that the central maximum now lies at a point where $$5th$$ bright fringe was lying earlier (before inserting the slab). Wavelength of light used is $$5000\mathring{A}$$.

A
$$5 \times 10^{-6}m $$

B
$$3 \times 10^{-6}m$$

C
$$10 \times 10^{-6}m$$

D
$$5 \times 10^{-5}m$$

Solution

According to the question,
Shift in the central maximum = $$ \triangle x$$ (path difference) of the 5th bright fringe

$$\dfrac{(\mu-1)tD}{d} = \dfrac{5\lambda D}{d}$$

$$t = \dfrac{5 \lambda}{( \mu -1)}$$ [Given $$\lambda$$ = 5000 $$ \mathring {A }$$ and $$ \mu = 1.5$$]
= $$ 5 \times 10^{-6}$$ m
Question 8
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Light is incident at an angle $$\phi$$ with the normal to a plane containing two slits of separation d. Select the expression that correctly describes the positions of the interference maxima in terms of the incoming angle $$\phi$$ and outgoing angle $$\theta$$.

A
$$sin\phi +sin\theta=\left(m+\dfrac{1}{2}\right)\dfrac{y}{d}$$

B
$$d sin \theta= m\lambda$$

C
$$ sin \phi-sin \theta=(m+1)\dfrac{\lambda}{d}$$

D
$$ sin \phi + sin \theta= m\dfrac{\lambda}{d}$$

Solution

We see in the problem that the path cover by lower ray is greater than that of the path covered by the upper ray. Since both the rays go in same direction and have path difference before and after the slit.
Path difference before the slit = $$ \triangle x$$ = d$$sin\phi$$
Path difference after the slit = $$ \triangle x$$ = d$$sin\theta$$
Path difference= $$d sin\phi + d sin \theta $$
For maxima, $$\triangle x=m\lambda$$
$$\Rightarrow sin\phi+ sin\theta=\dfrac{m\lambda}{d}$$
Question 9
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A plane wavefront travelling in a straight line in a vacuum encounters a medium of refractive index $$m$$. At $$P$$, the shape of the wavefront is

A

B

C

D

Solution

Velocity of wave in medium $$(\mu)$$ is less than that in air.
$$\therefore$$Wavefront reaches earlier at $$P$$ through air.
Hence, option B is the correct shape of the wavefront.
Question 10
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Given figure shows two coherent sources $$S_{1}$$ and $$S_{2}$$ vibrating in same phase. AB is an irregular wire lying at a far distance from the sources $$S_{1}$$ and $$S_{2}$$. Let $$\dfrac{\lambda}{d}=10^{-3} \angle BOA ={0.12^\circ}$$. How many bright spots will be seen on the wire, including points $$A$$ and $$B$$?

A
$$ 2 $$

B
$$3$$

C
$$4$$

D
more than 4

Solution

Here bright spots mean no. of maxima in between $$\angle BOA$$ = $$0.12 ^\circ$$.
Angular width=$$\dfrac{\lambda}{d}=10^{-3}$$ (given)

No. of fringes within $$0.12^{\circ}$$ will be

$$n=\dfrac{0.12\times 2\pi}{360 \times 10^{-3}} \cong [2.09]$$

The number of bright spots will be three.