Angle of minimum deviation for a prism refractive index 1.5...

Angle of minimum deviation for a prism refractive index $1.5$ is equal to the angle of the prism. Then the angle of prism (given, $\sin 48^{\circ} 36^{\prime}=0.75$ )
(A) $62^{\circ}$
(B) $82^{\circ}$
(C) $60^{\circ}$
(D) $41^{\circ}$

Key Concepts

Minimum Deviation

The minimum deviation condition in a prism is achieved when the light ray traverses the prism symmetrically; that is, the angle of incidence equals the angle of emergence. This makes the internal angle of refraction at both surfaces equal, simplifying the analysis of the light’s path through the prism and the resulting relationship between the deviation angle and the prism angle.

Refractive Index

The refractive index is a measure of how much a light ray bends when it enters a medium. It is defined as the ratio of the speed of light in vacuum to that in the medium. In the context of a prism, the refractive index directly influences how the angle of the light ray changes at the boundaries, playing a key role in calculating angles and deviations using Snell’s law.

Snell’s Law in Prisms

Snell’s law relates the sine of the angle of incidence to the sine of the angle of refraction, scaled by the refractive indices of the two media. Applied to a prism, and especially under the condition of minimum deviation, it provides a relationship that connects the refractive index, the prism angle, and the deviation angle, thereby allowing one to compute unknown angles when the refractive index is known.

Trigonometric Identities in Optics

Trigonometric identities, such as the double-angle formula (for example, expressing sinA in terms of sin(A/2) and cos(A/2)), are crucial in simplifying the equations that emerge from applying Snell’s law in the analysis of prismatic systems. These identities help in re-expressing complex trigonometric relationships into simpler forms, which makes solving for the prism’s angle or deviation more tractable.

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