The ratio of resolving powers of an optical microscope for two wavelengths ${\lambda }_1=4000 \stackrel{o}{A } and {\lambda }_2=6000 \stackrel{o}{A}$ is:

1. 8:27

2. 9:4

3. 3:2

4. 16:81

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 $\dot{A}$ is incident on the slit. The first secondary maximum is observed is an angle of 

(1) ${\sin }^{-1}\left(\frac{2}{3}\right)$

(2) ${\sin }^{-1}\left(\frac{1}{2}\right)$

(3) ${\sin }^{-1}\left(\frac{3}{4}\right)$

(4) ${\sin }^{-1}\left(\frac{1}{4}\right)$

At the first minimum adjacent to the central maximum of a single slit diffraction pattern, the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint of the slit is

(1) π/4 radian

(2) π/2 radian

(3) π radian

(4) π/8 radian

A thin mica sheet of thickness 2×10^–6 m and refractive index (μ = 1.5) is introduced in the path of the first wave. The wavelength of the wave used is 5000 Å. The central bright maximum will shift 

(1) 2 fringes upward

(2) 2 fringes downward

(3) 10 fringes upward

(4) None of these

In Young's double slit experiment, the distance between the two slits is 0.1 mm and the wavelength of light used is 4×10^–7 m. If the width of the fringe on the screen is 4 mm, the distance between screen and slit is 

(1) 0.1 mm

(2) 1 cm

(3) 0.1 cm

(4) 1 m

In Young’s experiment, the distance between slits is 0.28 mm and distance between slits and screen is 1.4 m. Distance between central bright fringe and third bright fringe is 0.9 cm. What is the wavelength of used light 

(1) 5000 Å

(2) 6000 Å

(3) 7000 Å

(4) 9000 Å

If a transparent medium of refractive index μ = 1.5 and thickness t = 2.5 × 10^–5 m is inserted in front of one of the slits of Young’s Double Slit experiment, how much will be the shift in the interference pattern? The distance between the slits is 0.5 mm and that between slits and screen is 100 cm 

(1) 5 cm

(2) 2.5 cm

(3) 0.25 cm

(4) 0.1 cm

In Young’s experiment, monochromatic light is used to illuminate the two slits A and B. Interference fringes are observed on a screen placed in front of the slits. Now if a thin glass plate is placed normally in the path of the beam coming from the slit 

(1) The fringes will disappear

(2) The fringe width will increase

(3) The fringe width will decrease

(4) There will be no change in the fringe width but the pattern shifts

In Young’s double-slit experiment the wavelength of light was changed from 7000 Å to 3500 Å. While doubling the separation between the slits which of the following is not true for this experiment:

(1) The width of the fringes changes

(2) The colour of bright fringes changes

(3) The separation between successive bright fringes changes

(4) The separation between successive dark fringes remains unchanged

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