Question

If instead of $Mg{F}_2$, the coating of the substance whose refractive indices is larger than the refractive index of glass was made then interference

• A. would not have occurred
• B. would have occurred due to total internal reflection of light
• C. would have occurred due to refraction of light
• D. would have occurred due to strong reflection

Answer 1

The correct option is B would have occurred due to total internal reflection of light

A phase change of ${180}^o$ occurs due to reflection from a higher refractive index surface.

Therefore there is a phase change of ${180}^o$ in the ray AA1 from the original ray when the coating is $Mg{F}_2$. Also the initial ray travels to point B for a phase change of ${180}^o$ due to reflection from glass and then again a phase lag of ${180}^o$ due to the extra path(ABC) covered. Hence the ray AA1 and CC1 have a net phase difference of ${180}^o$ and interfere destructively.

But when the refractive index of the coating is made greater than that of glass, no phase change occurs during reflection at B. Hence the rays AA1 and CC1 have no phase difference and interfere constructively.