Question

A parallel beam of sodium light of wavelength 5890 Å is incident on a thin glass plate of refractive index 1.5 such that the angle of refraction in the plate is 60⁰. The smallest thickness of the plate which will make it dark by reflection:

• A. 3926 Å
• B. 4353 Å
• C. 1396 Å
• D. 1921 Å

Answer 1

Answer: (A)

3926 Å

Answer 2

: the condition for minimum thickness corresponding to a dark band is

$2\mu t\cos r = \lambda$

$\therefore t = \frac{\lambda}{2\mu\cos r} = \frac{5890 \times 10^{- 10}}{2 \times 1.5 \times \cos 60{^\circ}}$

$= 3926 \times 10^{- 10}m = 3926Å$