Question

A ray of light is travelling through air. Find the thickness of a glass plate which will produce a change in optical path equal to one fourth of the wavelength $\left(\lambda \right)$ of light, passing normally through it. The refractive index of glass is $\mu$.

• A. $\frac{4(\mu -1)}{\lambda }$
• B. $\frac{\lambda }{4\mu }$
• C. $\frac{\lambda }{4(\mu -1)}$
• D. $\frac{4\mu }{\lambda }$

Answer 1

The correct option is C $\frac{\lambda }{4(\mu -1)}$

Consider two light waves, one travelling through air and the other through a glass slab of thickness $t$.

The change in optical path is equal to the path difference between the two waves, introduced due to the glass slab.

$\therefore \Delta x=(\mu -1)t$

Here, $\Delta x=\frac{\lambda }{4}$
$\therefore \frac{\lambda }{4}=(\mu -1)t$
$t=\frac{\lambda }{4(\mu -1)}$

Hence, $\left(C\right)$ is the correct answer.