Question

An equilateral prism is placed on a horizontal surface. A ray \[PQ\] is incident onto it. For minimum deviation:

A. \[PQ\] is horizontal
B. \[QR\] is horizontal
C. \[RS\] is horizontal
D. anyone will be horizontal

Answer 1

Hint:Angle of deviation in refraction is given by \[\left| {i - r} \right|\] where \[i\] is the incident angle and \[r\] is the reflected angle. The angle of deviation varies with the angle of incidence of the ray incident on the first refracting face of the prism. For the minimum angle of deviation, the angle of emergence and the angle of incidence must be equal.

Complete step by step answer:
The angle of deviation is defined as the angle which is obtained from the difference between the angle of incidence and the angle of refraction of the ray of light traveling from one medium to another medium. Angle of deviation in refraction is given by \[\left| {i - r} \right|\] where \[i\] is the incident angle and \[r\] is the reflected angle.

Now, for the minimum angle of deviation, the angle of emergence and the angle of incidence must be equal. Therefore, the refracting angles \[{r_1}\] and \[{r_2}\] must be equal.
Since the refracting angle is equal and the prism is equilateral the reflected ray from the first surface must be parallel to the base.

Thus, the ray \[QR\] must be parallel to the base of an equilateral triangle. \[QR\] is horizontal.

Therefore, the correct answer is option B.

Note:As we increase the angle of incidence the angle of deviation first decreases, and the angle of deviation reaches its minima when the angle of incidence is equal to the angle of emergence. After further increasing the angle of incidence the angle of deviation again starts increasing.