Question

A parallel beam of sodium light of wavelength $6000\mathring{A}$ is incident on a thin glass plate of refractive index $1.5$ such that the angle of refraction in the plate is $60^{\circ }$. The smallest thickness of the plate which will make it dark by reflection.

• A. $4000\mathring{A}$
• B. $4200\mathring{A}$
• C. $1390\mathring{A}$
• D. $2220\mathring{A}$

Answer 1

Answer: (A)

The condition for minimum thickness corresponding to a dark band in reflection
$2\mu t\cos r-\lambda$
$\therefore t=\frac{\lambda }{2\mu \cos r}=\frac{6000\times 10^{-10}}{2\times 1.5\times \cos 60^{\circ }}$
$=4000\mathring{A}$