In two separate set-ups of the Young's double slit experiment, fringes of equal width are observed when lights of wavelengths in the ratio \(1:2\) are used. If the ratio of the slit separation in the two cases is \(2:1\), the ratio of the distances between the plane of the slits and the screen in the two set-ups is:
1. \(4:1\)
2. \(1:1\)
3. \(1:4\)
4. \(2:1\)

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

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. \(8~\text{rad}\)

A beam of light of wavelength 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first dark fringes on either side of the central bright fringe is 

(1) 1.2 mm

(2) 1.2 cm

(3) 2.4 cm

(4) 2.4 mm

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. \(60^{\circ}\)

When an unpolarized light of intensity I₀ is incident on a polarizing sheet, the intensity of the light which does not get transmitted is:
1. Zero
2. \(I_0\)
3. \(\dfrac{I_0}{2}\)
4. \(\dfrac{I_0}{4}\)

When the angle of incidence on a material is 60°, the reflected light is completely polarized. The velocity of the refracted ray inside the material is (in ms^–1)

1. 3 × 10⁸

2. $\left(\frac{{\displaystyle 3}}{{\displaystyle \sqrt{2}}}\right)\times {10}^8$

3. $\sqrt{3}\times {10}^8$

4. 0.5 × 10⁸

In the ideal double-slit experiment when a glass-plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wavelength $\mathrm{\lambda }$), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is

1. 2$\mathrm{\lambda }$

2. 2$\mathrm{\lambda }$/3

3. $\mathrm{\lambda }$/3

4. $\lambda$

In Young's double-slit experiment, a point P on the central bright fringe is such that the intensity the point P is 1/4 time the maximum intensity. The distance between the slits is d and the wavelength is $\mathrm{\lambda }$. Then angular separation of point P is

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

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

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

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