Question

A ray of light travels from a medium of refractive index $\mu$ to air. Its angle of incidence in the medium is $i$, measured from the normal to the boundary, and its angle of deviation is $\delta .\delta$ is plotted against $i$. Which of the following best represents the resulting curve?

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

The ray of light is refracted at the plane surface.
However, since the ray is travelling from a denser to a rarer medium, for an angle of incidence $(i)$ greater then the critical angle $(c)$ the ray will be totally internally reflected.

For $i<c$, deviation $\delta =r-i$ with $\frac{1}{\mu }=\frac{\sin i}{\sin r}$
Hence $\delta ={\sin }^{-1}(\mu \sin i)-i$
This is a non - linear relation. The maximum value of $\delta$ is ${\delta }_1=\frac{\pi }{2}-c$,

where $i=c$ and $\mu =\frac{1}{\sin c}$
For $i>c$, deviation $d=\pi -2i$
$\delta$ decreases linearly with $i$.
${\delta }_2=\pi -2c=2{\delta }_1$