In Young’s double-slit experiment, an interference pattern is obtained on a screen by a light of wavelength 6000 Å, coming from the coherent sources S₁ and S₂. At certain point P on the screen third dark fringe is formed. Then the path difference S₁P – S₂P in microns is 

(1) 0.75

(2) 1.5

(3) 3.0

(4) 4.5

In Young’s double-slit experiment the fringe width is β. If entire arrangement is placed in a liquid of refractive index n, the fringe width becomes 

(1) $\frac{\beta }{n+1}$

(2) nβ

(3) $\frac{\beta }{n}$

(4) $\frac{\beta }{n-1}$

In Young’s double slit experiment, distance between two sources is 0.1 mm. The distance of screen from the sources is 20 cm. Wavelength of light used is 5460 Å. Then angular position of the first dark fringe is 

1. 0.08°

2. 0.16°

3. 0.20°

4. 0.32°

In a Young’s double slit experiment, the slit separation is 0.2 cm, the distance between the screen and slit is 1m. Wavelength of the light used is 5000 Å. The distance between two consecutive dark fringes (in mm) is 

(1) 0.25

(2) 0.26

(3) 0.27

(4) 0.28

A star emitting light of wavelength 5896 Å is moving away from the earth with a speed of 3600 km/sec. The wavelength of light observed on earth will 

(1) Decrease by 5825.25 Å

(2) Increase by 5966.75 Å

(3) Decrease by 70.75 Å

(4) Increase by 70.75 Å

(c = 3 × 10⁸ m/sec is the speed of light)

A heavenly body is receding away from the earth such that the fractional change in λ is 1, then its velocity is :

(1) C

(2) $\frac{3C}{5}$

(3) $\frac{C}{5}$

(4) $\frac{2C}{5}$

What will be the angular width of central maxima in Fraunhoffer diffraction when light of wavelength \(6000~\mathring{A}\) is used and slit width is \(12\times 10^{-5}\) cm:
1. \(2~\text{rad}\)
2. \(3~\text{rad}\)
3. \(1~\text{rad}\)
4. \(8~\text{rad}\)

The direction of the first secondary maximum in the Fraunhofer diffraction pattern at a single slit is given by:
\((a\) is the width of the slit) 
1. \(a\sin\theta = \frac{\lambda}{2}\)
2. \(a\cos\theta = \frac{3\lambda}{2}\)
3. \(a\sin\theta = \lambda\)
4. \(a\sin\theta = \frac{3\lambda}{2}\)

A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the edges of the slit is:
1. \(0\)
2. \(\dfrac \pi 2 \)
3. \(\pi\)
4. \(2\pi\)

A parallel beam of monochromatic light of wavelength \(5000~\mathring{A}\) is incident normally on a single narrow slit of width \(0.001\) mm. The light is focused by a convex lens on a screen placed on the focal plane. The first minimum will be formed for the angle of diffraction equal to:
1. \(0^{\circ}\)
2. \(15^{\circ}\)
3. \(30^{\circ}\)
4. \(60^{\circ}\)