Question

A glass plate of refractive index $1.5$ is coated with a thin layer of thickness $t$ and refractive index $1.8$. Light of wavelength $\lambda$ travelling in air is incident normally on the layer. It is partly reflected at the upper and the lower surfaces of the layer and the two reflected rays interfere. Write the condition for their constructive interference. If $\lambda =648nm$, obtain the least value of $t$ for which the rays interfere constructively.

• A. $90nm$
• B. $40nm$
• C. $30nm$
• D. $45nm$

Answer 1

The correct option is A $90nm$

$\text{Given}:$ $\mu \left(glass\right)=1.5$, $\mu \left(thinlayer\right)=1.8$, $\lambda =648nm$

$\text{Solution}"$

Path difference between rays reflected from upper and lower faces of layer $=2\mu t$ (for normal incidence)

Path difference due to reflection form denser (upper) surface Is $\frac{\lambda }{2}$.

condition of constructive interference (or maxima) is

$2\mu t+\frac{\lambda }{2}=n\lambda t=\frac{1}{2\mu }(2n-1)\frac{\lambda }{2}=\frac{(2n-1)\lambda }{4\mu }$ , n = 1, 2, 3,...

For least thickness, n = 1.

$\therefore t_{min}=\frac{\lambda }{4\mu }=\frac{648}{4\times 1.8}nm=90nm$

$\text{Hence A is the correct option}$