The Effect of Path Difference

Q. In a Young's double slit experiment, the slits are $2\text{mm}$ apart and are illuminated by photons of two wavelengths ${\lambda }_1=12000\mathring{\text{A}}$ and ${\lambda }_2=10000\mathring{\text{A}}$. At what minimum distance from the common central bright fringe on the screen, $2\text{m}$ from the slit, will a bright fringe from one interference pattern coincide, with a bright fringe from the other?

1. $3\text{mm}$
2. $8\text{mm}$
3. $6\text{mm}$
4. $4\text{mm}$

Q.

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is $5m$, while the distance between one crest and one trough is $1.5m$. The possible wavelengths (in $m$) of the waves are:

1. $1,3,5,\dots ..$

2. $1,2,3,\dots ..$

3. $\frac{1}{2},\frac{1}{4},\frac{1}{6}......$

4. $\frac{1}{1},\frac{1}{3},\frac{1}{5}$

Q. The angular width of the central maximum in a single sit diffraction pattern is ${60}^{\circ }.$ The width of the slit is $1\mu m$. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance $50cm$ from the silts. If the observed fringe width is $1cm,$ what is slit separation distance? (i.e. distance between the centres of each slit)

1. $75\mu m$
2. $100\mu m$
3. $25\mu m$
4. $50\mu m$

Q. When a drop of oil is spread on a water surface, it displays beautiful colours in daylight because of

1. dispersion of light.
2. reflection of light.
3. polarization of light.
4. interference of light.

Q.

When one of the slits in Young's experiment is covered with a transparent sheet of thickness $3.6\times {10}^{-3}$ cm the central fringe shifts to a position originally occupied by the 30th brigth fringe. If $\lambda =6000A,$ the refractive index of the sheet is

1. 1.50
   

2. 1.65

3. 1.55
   

4. 1.60
   

Q.

In a double slits interference experiment, the separation between the slits is 1.0 mm, the wavelength of light used is $5.0\times {10}^{-7}$ m and the distance of the screen from the slits is 1.0 m (a0 Find the distance of the centre of the first minimum from the centre of the central maximum. (b) how many bright fringes ar formed in one ventimetr width on the screen?

Q. $S_1$ and $S_2$ are two coherent sources of sound of frequency $110\text{Hz}$ each and have no initial phase difference. The intensity at a point P due to $S_1$ is $I_0$ and due to $S_2$ is $4I_0$. If the velocity of sound is $330\text{m/s}$, then the resultant intensity at P is

1. $I_0$
2. $9I_0$
3. $3I_0$
4. $8I_0$

Q. Read the assertion and reason carefully to mark the correct option out of the options given below.

Assertion: When a tiny circular obstacle is placed in the path of light from some distance, a bright spot is seen at the center of shadow of the obstacle.

Reason: Destructive interference occurs at the center of the shadow.

1. Both assertion and reason are true, and the reason is the correct explanation of the assertion.
2. Both assertion and reason are true, but reason is not the correct explanation of the assertion.
3. Assertion is true, but reason is false.
4. Assertion and reason both are false.

Q.

A laser beam is coherent because it contains

1. waves of several wavelengths.

2. incoherent waves of a single wavelength.

3. coherent waves of several wavelengths

4. coherent waves of a single wavelength.

Q.

The observed wavelength of light coming from a distant galaxy is found to be increased by $0.5\%$ as compared with that coming from a terrestrial source. The galaxy is

1. receding earth with a speed equal to $5\times {10}^5\text{m/s}$.
2. approaching earth with a speed equal to $5\times {10}^5\text{m/s}$.
3. approaching earth with a speed equal to $1.5\times {10}^6\text{m/s}$.
4. receding earth with a speed equal to $1.5\times {10}^6\text{m/s}$.

Q.

What is the interference of waves?

Q. Monochromatic light of wavelength $640\text{nm}$ falls normally on a glass plate of refractive index $\mathrm{1.6.}$ The waves reflected from the upper and lower faces of the film will interfere constructively if the least thickness of the plate is .

1. $100\text{nm}$
2. $200\text{nm}$
3. $300\text{nm}$
4. $400\text{nm}$

Q.

A vessel contains water up to a height of 20 cm and above it an oil up to another 20 cm. The refractive indices of the water and the oil are 1.33 and 1.30 respectively. Find the apparent depth of the vessel when viewed from above.

Q.

If any explosion takes place at the bottom of a lake, what type of shock waves in water will take place?

Q. A parallel beam of light of the wavelength 560 nm falls on a thin film of oil (refractive index 1.4). what should be the minimum thickness of the film so that it strongly reflects the light?

1. 100 nm
2. 400 nm
3. 200 nm
4. 300 nm

Q. Two SHMs are represented by y=asin(wt-kx) and y=bcos(wt-kx).the phase difference between two is

Q. The intensity of each of the two slits in Young's double slit experiment is $I_0$. Calculate the minimum separation between the two points on the screen where intensities are $2I_0$ and $I_0$. Given, the fringe width equal to $\beta$.

1. $\frac{\beta }{4}$
2. $\frac{\beta }{3}$
3. $\frac{\beta }{12}$
4. $\beta$

Q.

Can two identical and independent sodium lamps act as coherent sources?

Q.

Which of the following is a unique property of laser?

1. directional

2. speed

3. coherence

4. wavelength

Q. The ratio of intensities between two coherent sound sources is $9:1$. The difference of loudness in decibels $\left(\text{dB}\right)$ between maximum and minimum intensities when they interfere in space is

1. $10\log 4$
2. $10\log 9$
3. $10\log 3$
4. $\log 3$

Q.

A thin paper of thickness 0.02 mm having a refractive index 1.45 is pasted across one of the slits in a young's double slit experiment. The paper transmits $\frac{4}{9}$ of the light energy falling on it. (a) Find the rationof te maximum intensity to the minimum intensity in the fringe pattern. (b) how many fringes will cross through the centre if an identical paper piece is pasted on the other slit also, The wavelength of the light used is 600 nm.

Q. A plane monochromatic light wave falls normally on a diaphragm with two narrow slits separated by $2.5\text{mm}$. The fringe pattern is formed on a screen $100\text{cm}$ behind the diaphragm. By what distance will these fringes be displaced, when one of the slits is covered by a glass plate $(\mu =1.5)$ of thickness $10\mu \text{m}$?

1. $2\text{mm}$
2. $1\text{mm}$
3. $3\text{mm}$
4. $4\text{mm}$

Q.

A small source of sound vibrating at frequency 500 Hz is rotated in a circle of radius $\frac{100}{\pi }$ cm at a constant angular speed of 5.0 revolutions per second. A listener situates himself in the plane of the circle. Find the minimum and the maximum frequency of the sound observed. Speed of sound in air $=332m{s}^{-1}$.

Q. A sound consists of four frequencies : $200\text{Hz},400\text{Hz},1125\text{Hz}$ and $1600\text{Hz}$. A sound filter is made by passing this sound through a bifurcated pipe as shown. The sound wave has to travel a distance $40\text{cm}$ more in the right branch than in the straight pipe. The speed of sound in air is $300\text{m/s}$. which of the given frequencies will almost completely muffle or silence the outlet?

1. $200\text{Hz}$
2. $400\text{Hz}$
3. $1125\text{Hz}$
4. $1600\text{Hz}$

Q. Two persons A and B, each carrying a source of sound of frequency $f$, are standing a few metres apart in a quiet field. A starts moving towards B with a speed $u$. If $v$ is the speed of sound, the number of beats heard per second by A will be

1. $\frac{fu}{v}$
2. $\frac{2fu}{v}$
3. $\frac{fu}{(v+u)}$
4. $\frac{fu}{(v-u)}$

Q. Slit width in a Young's double slit experiment are in the ratio $9:4$. The ratio of intensity at minima to that at maxima, is

1. $4:9$
2. $16:81$
3. $1:25$
4. $1:5$

Q. 17. Draw the intensity pattern for single slit diffraction and double slit interference. Hence, state two differences between interference and diffraction patterns

Q.

A source emitting light of wavelengths 480 nm and 600 nm is used in a double slit interference experiment. The separation between the slit is 0.25mm and the interference is observed ona screen placed at 150 cm from the slits. Find th linear separation between the first maximum (next ot the central maximum) corresponding to he two wavelengths.

Q. When interference of light takes place

1. Energy is created in the region of maximum intensity
2. Conservation of energy holds good and energy is redistributed
3. Energy is destroyed in the region of maximum intensity
4. Conservation of energy doesnt hold good

Q. Two speakers $S_1\text{and}{S}_2$ are derived from the same amplifier and placed at the same distance from $x$-axis as shown in figure. The speakers vibrate in phase at $680\text{Hz}$. A man stands at a point on the $x$-axis at a very large distance from the origin and starts moving parallel to the $y$-axis. The speed of sound is $340\text{m/s}$. Then, at what angle $\theta$ with the $x-$ axis will the intensity of sound drop to a minimum for the first time?

1. ${5.4}^{\circ }$
2. ${9.3}^{\circ }$
3. ${7.2}^{\circ }$
4. ${3.6}^{\circ }$