Question

In Young's double slit experiment using monochromatic light the fringe pattern shifts by a certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 1.964 microns is introduced in the path of one of the interfering waves. The mica sheet is then removed and the distance between the plane of the slits and the screen is doubled. It is found that the distance between successive maxima (or minima) now is the same as the observed fringe shift upon the introduction of the mica sheet. Calculate the wavelength of the light?

• A. 5.892 Å
• B. 5692 Å
• C. 5892 Å
• D. 5800 Å

Answer 1

Answer: (C)

5892 Å

Answer 2

l = ?

When mica sheet of thickness t and refractive index µ is introduced in the path of one of the interfering beams, optical path increases by (µ – 1)t,

\ the shift on the screen

y₀ =$\frac{D}{d}$ (µ – 1)t … (1)

When the distance between the plane of slits and screen is changed from D to 2D, then

b =$\frac{2D}{d}$l … (2)

\ $\frac{D}{d}$ (µ _ 1)t =$\frac{2D(\lambda)}{d}$̃ l =$\frac{1}{2}$ (µ – 1)t =$\frac{1}{2}$ (1.6 – 1) × 1.964 × 10^–6 m = 5892 Å

Therefore the answer is (3).