Question

A ray of light incident at an angle $\alpha$ on the boundary separating two transparent media. It is transmitted. When angle $\alpha$ is increased very slightly (by negligible amount), the ray suffers a total internal reflection. The difference between the angles of deviation in two cases is

• A. $2\alpha$
• B. ${90}^{\circ }-\alpha$
• C. ${180}^{\circ }-\alpha$
• D. ${180}^{\circ }-2\alpha$

Answer 1

Answer: (B)

${90}^{\circ }-\alpha$

Answer is B.
A ray of light incident normally to the medium goes undeviated along the same path. As the angle of incidence i increases, the angle of refraction r also increases.
On increasing the angle of incidence for a particular value say $i=C$ (critical angle), the angle of refraction r is found to be $90$ degrees.
Critical angle is the angle of incidence beyond which rays of light passing through a denser medium to the surface of a less dense medium are no longer refracted but totally reflected.
When $i>C$, the ray is reflected into the denser medium itself. This phenomenon is called total internal reflection.
Therefore, the angle of refraction = angle of deviation = 90 degrees when the total internal reflection occurs.
In this case, a ray of light is incident at an angle $\alpha$ on the boundary separating two transparent media, and it suffers a total internal reflection when the angle is increased slightly.
Hence, the difference between the angles of deviation in two cases is ${90}^o-\alpha$.