Question

A ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true? (A) RS is horizontal (B) either \(\mathrm{PQ}\) or \(\mathrm{RS}\) is horizontal (C) QR is horizontal (D) PQ is horizontal

Short answer

For minimum deviation in an equilateral glass prism, the angle of incidence and angle of emergence must be equal and symmetrical with respect to the base of the prism. In this case, the side PQ should be horizontal. Therefore, the correct statement is (D) PQ is horizontal.

Step-by-step solution

Define minimum deviation

Minimum deviation is the smallest angle through which a ray of light changes its direction when passing through a prism. This occurs when the angle of incidence and angle of emergence are equal. Step 2: Draw a diagram

Draw a diagram

Draw an equilateral triangle (with all angles equal to 60 degrees) representing the prism on a horizontal table. Mark points P, Q, and R at different corners of the triangle. Show the incident light ray entering the prism at point P, refracting inside, and emerging at point R. Draw QRS and PQ parallel to the table. Step 3: Analyze the given options

Analyze the given options

We have to determine which of the following options is true for minimum deviation: (A) RS is horizontal (B) either PQ or RS is horizontal (C) QR is horizontal (D) PQ is horizontal Step 4: Relation between minimum deviation and horizontal sides

Relation between minimum deviation and horizontal sides

For minimum deviation, the angle of incidence and angle of emergence have to be equal and thus symmetrical with respect to the base of the prism. In an equilateral prism, the angle of refraction inside the prism will be equal for both surfaces (PQ and RS). Hence, the incidence surface and emergence surface should be symmetrical to have equal angles of incidence and emergence. Step 5: Choose the correct option

Choose the correct option

For the prism to have symmetrical angles for minimum deviation, the side PQ should be horizontal. Thus, the answer is: (D) PQ is horizontal