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 $648$ nm travelling in air is incident normally on the layer. It is partly reflected at upper and lower surfaces of the layer and the rays interfere constructively is?

• A. $30$ nm
• B. $60$ nm
• C. $90$ nm
• D. $120$ nm

Answer 1

The correct option is C $90$ nm

Incident ray $AB$ is partly reflected as ray $1$ from the upper surface and partly reflected as ray $2$ from the lower surface of the layer of thickness $t$ and refractive index ${\mu }_1=1.8$ as shown in figure path difference between the two rays would be $\Delta x=2{\mu }_{1}t=2\left(1.8\right)t=3.6t$

Ray $1$ is reflected from a denser medium, therefore, it undergoes a phase change $\pi$ whereas the ray $2$ gets reflected from a rarer medium, therefore, there is no change in phase of ray $2$.

For constructive interference

$\Delta x=\left(n-\frac{1}{2}\right)\lambda ,$, where $n$=1,2,3,4...................

or $3.6t=\left(n-\frac{1}{2}\right)\lambda$

lest value of $t$ is corresponding to $n=1$ or $tmin=\frac{2}{2\times 3.6}$ or $tmin=\frac{648}{7.2}nm$

or

$tmin=90nm$.