Interference General Case

Q. The interference pattern is obtained with two coherent light sources of intensity ratio $n$. In the interference pattern, the ratio $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$ will be

1. $\frac{2\sqrt{n}}{(n+1{)}^2}$
2. $\frac{\sqrt{n}}{n+1}$
3. $\frac{2\sqrt{n}}{n+1}$
4. $\frac{\sqrt{n}}{(n+1{)}^2}$

Q. A taut string fixed at both ends vibrates in $2^{\text{nd}}$ overtone. The distance between adjacent node and antinode is found to be d. If the length of the string is $L$, then value of $\frac{L}{d}$ is

1. 6
2. 5
3. $\frac{11}{2}$
4. $\frac{7}{2}$

Q. The intensity of light emerging from one of the slits in a Young's double slit experiment is found to be 1.5 times the intensity of light emerging from the other slit. What will be the approximate ratio of intensity of an interference maximum to that of an interference minimum?

1. 2.25
2. 98
3. 5
4. 9.9

Q. Two coherent sources of intensity ratio 1 : 4 produce an interference pattern. The fringe visibility will be

1. 1
2. 0.8
3. 0.6
4. 0.4

Q. The contrast in the bright and dark fringes in any interference pattern depends on

1. Fringe width.
2. Wavelength.
3. Intensity ratio of the sources.
4. Distance between the sources.

Q. What is the maximum intensity of interference of $n$ identical waves each of intensity $I_0$, if the sources are coherent and incoherent respectively.

1. $n^2{I}_0,n^2{I}_0$
2. $n{I}_0,n{I}_0$
3. $n{I}_0,n^2{I}_0$
4. $n^2{I}_0,n{I}_0$

Q.

A plane wave of monochromatic light falls normally on a uniform thin film of oil which covers a glass plate. The wavelength of sources can be varied continuously. Complete destructive refraction is observed for $\lambda =5000\dot{A}$ and $\lambda =7000\dot{A}$ and for no other wavelength in between. If $\mu$ of oil is 1.3 and that of glass is 1.5, the thickness of the film will be

1. $6.378\times {10}^{-5}cm$
2. $5.7\times {10}^{-5}cm$
3. $4\times {10}^{-5}cm$
4. $2.8\times {10}^{-5}cm$

Q. Two waves of equal frequencies have their amplitudes in the ratio of $3:5$. They are superimposed on each other. The ratio of maximum and minimum intensities of the resultant wave is

1. $16:1$
2. $1:16$
3. $8:1$
4. $1:8$

Q.

Light from two source, each of same frequency and travelling in same direction, but with intensity in the ratio 4 :1 interfere. Find ratio of maximum to minimum intensity.

1. 1:1

2. 16:1

3. 9:1

4. 4:1

Q. Two identical speakers, emit sound waves of frequency ${10}^3\text{Hz}$ uniformly in all directions.
The audio output of each speaker is $\frac{9\pi }{10}\text{mW}$. A point $P$ is at a distance of $3\text{m}$ from $S_1$ and $5\text{m}$ from $S_2$. Resultant intensity of sound at $P$ is

1. $34\mu W/m^2,$ if the sources are incoherent.
2. $4\mu W/m^2,$ if the sources are coherent but out of phase.
3. $25\mu W/m^2,$ if $S_1$ is switched off.
4. $64\mu W/m^2,$ if the sources are coherent and in phase.

Q. A monochromatic light source $\text{S}$ of wavelength $440\text{nm}$ is placed slightly above a plane mirror $\text{M}$ as shown. Image of $\text{S}$ in $\text{M}$ can be used as a virtual source to produce interference fringes on the screen. The distance of source $\text{S}$ from $\text{O}$ is $20.0\text{cm}$, and the distance of screen from $\text{O}$ is $100.0\text{cm}$ (figure is not to scale). If the angle $\theta =0.50\times {10}^{-3}\text{radian}$, the width of the interference fringes observed on the screen is

1. $2.20\text{mm}$
2. $2.64\text{mm}$
3. $1.10\text{mm}$
4. $0.5\text{mm}$

Q. Determine the magnitude of the resultant amplitude for the interference of two similar waves when the phase difference between them is ${45}^{\circ }$. Given that, amplitudes of both sources are $A_1=3\text{cm},A_2=4\text{cm}$.

1. $3.5\text{cm}$
2. $4.5\text{cm}$
3. $6.5\text{cm}$
4. $7.5\text{cm}$

Q. A very thin transparent film of soap solution $(thickness\to 0)$ is seen under reflection of white light. Then the colour of the film appear to be

1. Blue
2. Black
3. Red
4. Yellow

Q. In the interference of two waves with identical amplitudes $A_0$ and the intensity $I_0$, the resultant intensity at a point where the path difference between two waves is $\frac{\lambda }{3}$ will be

1. $I_0$
2. $2I_0$
3. $\sqrt{2}{I}_0$
4. $\sqrt{3}{I}_0$

Q. Two coherent sources of intensity ratio '$\alpha$' interfere. In interference pattern $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}=$

1. $\frac{2\alpha }{1+\sqrt{\alpha }}$
2. $\frac{1+\alpha }{2\alpha }$
3. $\frac{2\alpha }{1+\alpha }$
4. $\frac{2\sqrt{\alpha }}{1+\alpha }$

Q. For two waves, each of amplitude $A_0$ and frequency $f$, what is the resultant amplitude at a point where the phase difference between the waves is ${30}^{\circ }$?
Given, $\cos {15}^{\circ }=\frac{\sqrt{3}+1}{2\sqrt{2}}$

1. $A_0\sqrt{3}$
   
2. $A_0\frac{\sqrt{3}}{2}$
   
3. $A_0\left(\frac{\sqrt{6}-\sqrt{2}}{2}\right)$
   
4. $A_0\left(\frac{\sqrt{6}+\sqrt{2}}{2}\right)$
   

Q. In Young's experiment of double slit, the number of times the intensity of the central bright band greater than the individual intensity of the interfering waves :

1. $2$
2. $4$
3. $16$
4. $6$

Q. Sounds from two identical sources $S_{1}and{S}_2$ reach a point P directly in the same phase with net intensity $I_0$ .The power of S1 is now reduced to $64\%$ of its initial value, and the phase difference between $S_{1}and{S}_2$ is varied continuously. The maximum and minimum intensities now recorded at P are Imax and Imin respectively. Then

1. $I_{max}=0.81I_0,I_{min}=0.01I_0$
2. $I_{max}=0.64I_0,I_{min}=0.36I_0$
3. $I_{max}=0.36I_0,I_{min}=0.09I_0$
4. $I_{max}=0.64I_0,I_{min}=0.04I_0$

Q. Two waves interfere at a point. Vibrations due to the waves at that point can be represented by $y_1=4\sin \omega t$ and $y_2=3\sin (\omega t+\frac{\pi }{3})$. The amplitude of the resulting wave is nearly

1. 4
2. 3
3. 5
4. 6

Q. When two coherent waves interfere, the maximum and minimum intensities are in the ratio 25:16. Then,
a) the maximum and minimum amplitudes are in the ratio 5 : 4
b) the amplitudes of individual waves are in the ratio 9 : 1
c)the intensities of individual waves are in the ratio 41: 9
d) the intensities of individual waves are in the ratio 81 : 1

1. a, b and c are true
2. a, b and d are true
3. a and b are true
4. b and c are true

Q. Two coherent light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are :

1. $5I$ and $I$
2. $9I$ and $3I$
3. $9I$ and $I$
4. $5I$ and $3I$

Q. Two coherent sources of intensity ratio $\beta$ interfere, then $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$ is equal to

1. $\frac{\beta }{1+\beta }$
2. $\frac{2\sqrt{\beta }}{1+\beta }$
3. $\frac{2\sqrt{\beta }}{1+\sqrt{\beta }}$
4. $\frac{2\beta }{1+\sqrt{\beta }}$

Q. $\text{YDSE}$ is carried with two thin sheets of thickness $10.4\mu \text{m}$ each and refractive index ${\mu }_1=1.52$ and $\mu =1.40$ covering the slits $S_1$ and $S_2$ respectively. If white light of range $400\text{nm}$ to $780\text{nm}$ is used, then which wavelength will form maxima exactly at point $O$, the centre of the screen

1. $416\text{nm}$ only
2. $624\text{nm}$ only
3. $416\text{nm}$ and $624\text{nm}$ only
4. $400\text{nm}$ and $316\text{nm}$ only

Q. Two radio stations broadcast their program at the same amplitude A but at slightly different frequencies $n_1$ and $n_2$ such that $(n_1-n_2)={10}^{3}Hz$. A detector receives signals from both the stations simultaneously but only when intensity of signal is greater than $2A^2$. The time interval between two successive maxima will be :

1. ${10}^{-2}s$
2. ${10}^{-1}s$
3. ${10}^{◃}s$
4. ${10}^{-3}s$

Q. If the ratio of maximum to minimum intensity in beat is 49, then the ratio of amplitudes of two progressive wave trains

1. 7:1
2. 4:3
3. 49:1
4. 16:9

Q. A third polaroid is placed between $P_1$ and $P_2$ with its pass axis making an angle $\theta$ with the pass axis of $P_1$. Find a value of $\theta$ for which the intensity of light emerging from $P_2$ is $l_0/8$ where $l_0$ is the intensity of light on the polaroid $P_1$.

Q. Two sinusoidal plane waves of same frequencies having intensities $I_0$ and ${4I}_0$ are travelling in the same direction . The resultant intensity at a point at which waves meet with a phase difference of zero radian is

1. $I_0$
2. ${9I}_0$
3. ${5I}_0$
4. ${3I}_0$

Q. Two coherent lights beams of intensity $I$ and $4I$ are superposed. The minimum and maximum possible intensities in the resultant beam are :

1. $9I$ and $I$
2. $5I$ and $3I$
3. $9I$ and $3I$
4. $5I$ and $I$

Q. Two identical waves interfere at a point in the same medium having amplitudes $3\text{cm}$ and $5\text{cm}$. Which of the resultant amplitude is not possible?

1. $2\text{cm}$
2. $5\text{cm}$
3. $6\text{cm}$
4. $9\text{cm}$

Q.

The amplitude of the electric field in a parallel beam of light of intensity $2.0W{m}^{-2}$ is:

1. $19.4$ N/C
2. $38.8$ N/C
3. $4.85$ N/C
4. $77.9$ N/C