Irodov Problem 5.23

Physics · optics

Problem

A trihedral prism with refracting angle 60∘^\circ provides the least deflection angle 37∘^\circ in air. Find the least deflection angle of that prism in water.
Intuitive explanation

The key insight is that minimum deviation depends on the refractive index of the medium the light travels through, not just the prism's material. When light enters water instead of air, the relative refractive index between the prism and surrounding medium changes, which shifts the angle at which minimum deviation occurs. Use the minimum deviation formula n=sin⁡(A+δm2)sin⁡(A2)n = \frac{\sin\left(\frac{A+\delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} to find the prism's absolute refractive index from the air data, then recalculate δm\delta_m using the effective refractive index in water.

Intuitive explanation

The key insight is that minimum deviation depends on the refractive index of the medium the light travels through, not just the prism's material. When light enters water instead of air, the relative refractive index between the prism and surrounding medium changes, which shifts the angle at which minimum deviation occurs. Use the minimum deviation formula n=sin⁡(A+δm2)sin⁡(A2)n = \frac{\sin\left(\frac{A+\delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} to find the prism's absolute refractive index from the air data, then recalculate δm\delta_m using the effective refractive index in water.

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