Question

If \(i_ 1\) and \(i _2\) are the angle of incidence and angle of emergence due to a prism respectively, then at the angle of minimum deviation

• A. \(i _1 = i_ 2\)
• B. \(i_ 1 > i_ 2\)
• C. \(i _1 < i_ 2\)
• D. None of these

Answer 1

The Correct Option is A

In optics, when light passes through a prism and is refracted, it undergoes deviation. A special scenario occurs at the angle of minimum deviation, where the incident ray, refracted ray inside the prism, and the emergent ray are symmetrically disposed with respect to the surfaces of the prism.

At the angle of minimum deviation, a key characteristic is that the angle of incidence \(i_1\) and the angle of emergence \(i_2\) are equal. This symmetry simplifies the path of light through the prism, resulting in the minimum possible deviation of the light ray.

Mathematically, this can be represented as: \(i_1 = i_2\)

This equality arises because the light traverses the prism path symmetrically: the path inside the prism and the points of entering and exiting the medium are at equal angles.

Thus, the correct statement is: \(i_1 = i_2\)

Answer 2

When light passes through a prism, the angle of incidence is \( i_1 \) and the angle of emergence is \( i_2 \).

At the angle of minimum deviation, the path of the light ray through the prism is symmetrical.

This means the ray enters and exits the prism at equal angles with respect to the normal. So,

\( i_1 = i_2 \)

This condition corresponds to the minimum deviation, where the deviation angle is the smallest.

Final Answer: \( i_1 = i_2 \)