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

An equilateral prism is placed on a horizontal surface. A ray PQPQ is incident onto it. For minimum deviation:

A. PQPQ is horizontal
B. QRQR is horizontal
C. RSRS is horizontal
D. anyone will be horizontal

Explanation

Solution

Angle of deviation in refraction is given by ir\left| {i - r} \right| where ii is the incident angle and rr 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 ir\left| {i - r} \right| where ii is the incident angle and rr 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 r1{r_1} and r2{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 QRQR must be parallel to the base of an equilateral triangle. QRQR 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.