Minima in Diffraction

Q.

In a Young’s double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

Q.

If Youngs double-slit experiment is performed underwater, how would the observed interference pattern be affected?

Q.

The 6563 Å line emitted by hydrogen in a star is found to be red shifted by 15 Å. Estimate the speed with which the star is receding from the Earth.

Q. Yellow light is used in single slit diffraction experiment with slit width 0.6 mm. If yellow light is replaced by X-rays then the pattern will reveal

[IIT-JEE (Screening) 1999; MP PMT 2002; KCET 2003]

1. More number of fringes

2. Less number of fringes

3. That the central maxima is narrower

4. No diffraction pattern

Q.

How does wavelength affect diffraction?

Q.

Write Any Four The Necessary Conditions for Interference of light.

Q.

The light of wavelength 6328 Å is incident on a slit of width 0.2 mm perpendicularly, the angular width of central maxima will be

[MP PMT 1987; Pb. PMT 2002]

1. 0.09°

2. 0.72°

3. 0.18°

4. 0.36°

Q.

The diffraction of light is not easily noticed if

1. Apparatus are needed for noticing

2. The wave length of visible range is small

3. Size of ordinary objects are small

4. Light waves are transverse and longitudinal in nature

Q. Two slits in Young's experiment have widths in the ratio 81 : 1. What is the ratio of the amplitudes of light waves coming from them?

Q.

A monochromatic light of wavelength λ is incident normally on a narrow slit of width 'a' to produce a diffraction pattern on the screen placed at a distance 'D' from the slit. With the help of relevant diagram, deduce the conditions for obtaining maxima and minima on the screen.

Q. In Young's doubles slit experiment, the angular position of a point on the central maxima whose intensity is one fourth of maximum intensity, then

1. 
   ${\sin }^{-1}\left(\frac{\lambda }{d}\right)$
2. 
   ${\sin }^{-1}\left(\frac{\lambda }{2d}\right)$
3. 
   
   ${\sin }^{-1}\left(\frac{\lambda }{3d}\right)$
   
4. 
   ${\sin }^{-1}\left(\frac{\lambda }{4d}\right)$

Q. Both light and sound waves produce diffraction. It is more difficult to observe the diffraction with light waves because

1. Wavelength of light waves is far smaller
2. Light waves are transverse
3. Speed of light is far greater
4. Light waves do not require medium

Q. A slit of width $a$ is illuminated by white light. The first minima for red light $(\lambda =6500\mathring{\text{A}})$ will fall at $\theta ={30}^{\circ }$, when $a$ will be equal to,

1. $3200\mathring{\text{A}}$
2. $6.5\times {10}^{-4}\text{mm}$
3. $1.3\text{micron}$
4. $2.6\times {10}^{-4}\text{cm}$

Q. A parallel beam of light of wavelength $6000\dot{A}$ is incident normally on a slit of width $0.2\text{mm}$. The diffraction pattern is observed on a screen which is placed at the focal plane of a convex lens of focal length $50\text{cm}$. If the lens is placed close to the slit. The distance between the minimum on both sides of the central maximum will be

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

Q.

The intensity of light transmitted by the analyzer is maximum when?

Q. In the far field diffraction pattern of a single slit under polychromatic illumination, the first minimum with the wavelength ${\lambda }_1$ is found to be coincident with the third maximum at ${\lambda }_2$. Then, which of the following equality is true?

1. $3{\lambda }_1=0.3{\lambda }_2$
2. $3{\lambda }_1={\lambda }_2$
3. ${\lambda }_1=3.5{\lambda }_2$
4. $0.3{\lambda }_1=3{\lambda }_2$

Q. Assertion $\left(\text{A}\right)$ : We cannot observe the diffraction pattern from a wide slit illuminated by monochromatic light.

Reason $\left(\text{R}\right)$ : In diffraction pattern all the bright bands are not of the same intensity.

1. Both $\text{A}$ and $\text{R}$ are true and $\text{R}$ is the correct explanation of $\text{A}$.
2. Both $\text{A}$ and $\text{R}$ are true and $\text{R}$ is not the correct explanation of $\text{A}$.
3. $\text{A}$ is true and $\text{R}$ is false.
4. $\text{A}$ is false and $\text{R}$ is true.

Q.

What is the angular spread of the first minimum and the central maximum when diffraction is observed with 540 nm light through a slit of width 1mm?

1. 810 x 10^-6 rad

2. 270 x 10^-6 rad

3. 540 x 10^-6 rad

4. 1080 x 10^-6 rad

Q. Light of wavelength 600 nm is incident upon a single slit with width $4\times {10}^{–4}m$. The figure shows the pattern observed on a screen positioned 2 m from the slits. Determine the distance s.

1. 0.002 m
2. 0.003 m
3. 0.004 m
4. 0.006 m

Q. The maximum velocity of electrons emitted from a metal surface is v. When frequency of light falling on it is f. The maximum velocity when frequency becomes 4f is A. 2v B. > 2v C. < 2v D. Between 2v and 4v

Q. 82.In a double slit experiment the distance between the slit is d. the screen is at a distance D from the slit and lambda is wavelength of light used. If a dark fringe is formed opposite to a slit on the screen the order of fringe is

Q. In a diffraction pattern due to a single slit of width a, the first minimum is observed at an angle ${30}^{\circ }$ when light of wavelength $5000\stackrel{\circ }{A}$ is incident on the slit. The first secondary maximum is observed at an angle of

1. $si{n}^{-1}\frac{2}{3}$
2. $si{n}^{-1}\frac{1}{2}$
3. $si{n}^{-1}\frac{1}{4}$
4. $si{n}^{-1}\frac{3}{4}$

Q.

A is an essential condition for coherent sources. Here, A refers to

1. constant phase difference

2. equal amplitude

3. Both (a) and (b) are correct

4. Both (a) and (b) are incorrect

Q. in a single slit diffraction pattern red light of wavelength= 650nm is used and first minimum is found to lie at angle 15 the slit width a is

Q. A parallel beam of monochromatic light of wave length $600\text{nm}$, falls normally on a slit of width $0.5\text{mm}.$ The resulting diffraction pattern is observed on a screen, placed $50\text{cm}$ from the slit. The linear separation between the first minimum and the first maximum on the same side of the central maximum is,

1. $0.003\text{mm}$.
2. $0.03\text{mm}$.
3. $0.3\text{mm}$.
4. $3\text{mm}$.

Q. If the sodium light (yellow color) in Young's double slit experiment, is replaced by red light, the fringe width will,

1. decrease
2. increase
3. remain constant
4. first increase then decrease

Q.

In Fresnel diffraction, if the distance between the disc and the screen is decreased, the intensity of central bright spot will

1. Increase

2. Decrease

3. Remain constant

4. None of these

Q. Choose the correct statement(s) regarding single slit diffraction experiment.

1. Intensity of all bright fringes is the same.
2. Intensity of central bright fringe is maximum.
3. Intensity of all bright fringes is not same.
4. Angular width of all the maxima is same.

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

Q. In the figure, a parallel beam of light is incident on the plane of the slits of Young's double-slit experiment. Light incident on the slit $S_1$ passes through a medium of variable refractive index $\mu =1+ax$ (where $x$ is the distance from the plane of slits as shown), up to a distance $l$ before falling on $S_1$. The rest of the space is filled with air. If at $O$ minima is formed, then the minimum value of the positive constant $a$ ( in terms of $l$ and wavelength $\lambda$ in air) is

1. $\frac{\lambda }{l}$
2. $\frac{\lambda }{l^2}$
3. $\frac{l^2}{\lambda }$
4. $\frac{l}{\lambda }$