In Young's double slit experiment, if L is the distance between the slits and the screen upon which interference pattern is observed, x is the average distance between the adjacent fringes and d being the slit separation. The wavelength of light is given by 

(1) $\frac{xd}{L}$

(2) $\frac{xL}{d}$

(3) $\frac{Ld}{x}$

(4) $\frac{1}{Ldx}$

In Young's experiment, light of wavelength \(4000~\mathring{A}\) is used to produce bright fringes of width \(0.6\) mm, at a distance of \(2\) meters. If the whole apparatus is dipped in a liquid of refractive index \(1.5\), then fringe width will be:
1. \(0.2~\text{mm}\)
2. \(0.3~\text{mm}\)
3. \(0.4~\text{mm}\)
4. \(1.2~\text{mm}\)

In Young's double-slit experiment, the phase difference between the light waves reaching the third bright fringe from the central fringe will be (λ =6000 Å ) 

(1) Zero

(2) 2$\pi$

(3) 4$\pi$

(4) 6$\pi$

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. \(2:1\)

In a biprism experiment, by using light of wavelength 5000 Å, 5 mm wide fringes are obtained on a screen 1.0 m away from the coherent sources. The separation between the two coherent sources is

(1) 1.0 mm

(2) 0.1 mm

(3) 0.05 mm

(4) 0.01 mm

The slits in Young's double-slit experiment have equal widths and the source is placed symmetrically relative to the slits. The intensity at the central fringe is \(I_0\). If one of the slits is closed, the intensity at this point will be:
1. \(I_0\)
2. \(\frac{I_0}{4}\)
3. \(\frac{I_0}{2}\)
4. \(4I_0\)

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, 62 fringes are seen in visible region for sodium light of wavelength 5893 Å. If violet light of wavelength 4358 Å is used in place of sodium light, then number of fringes seen will be 

(1) 54

(2) 64

(3) 74

(4) 84

In Young's double slit experiment, the angular width of fringe is \(0.20^{\circ}\) for sodium light of wavelength \(5890~\mathring{A}\). The angular width of fringe, if the complete system is dipped in water, will be:
1. \(0.11^{\circ}\)
2. \(0.15^{\circ}\)
3. \(0.22^{\circ}\)
4. \(0.30^{\circ}\)

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