Find the Angle of Minimum Deviation for an Equilateral Triangle Prism Having Refractive Index 1.5. – Full Guide

In optics, the angle of minimum deviation for an equilateral triangle prism is an important concept that helps explain how light bends as it passes through a prism with known refractive index. This guide explains the concept and how to calculate it clearly.

What Is the Angle of Minimum Deviation?

The angle of minimum deviation is the smallest angle by which a light ray deviates when it passes through a prism. At this angle, the light path inside the prism is symmetric, making it useful for accurate refractive index measurements.

Calculating the Angle of Minimum Deviation for an Equilateral Prism

For an equilateral triangular prism, each angle of the prism (A) is 60°. The refractive index (µ) is given as 1.34.
The formula for minimum deviation (D_min) for any prism is:

µ = sin((A + D_min)/2) / sin(A/2)

Substituting known values:

A = 60°, µ = 1.34
sin(60°/2) = sin(30°) = 0.5
So, 1.34 = sin((60° + D_min)/2) ÷ 0.5
→ sin((60° + D_min)/2) = 1.34 × 0.5 = 0.67
(60° + D_min)/2 ≈ sin⁻¹(0.67) ≈ 42.1°
60° + D_min ≈ 84.2°
→ D_min ≈ 84.2° – 60° ≈ 24.2°

Note:
The angle of minimum deviation depends on both the prism angle and the refractive index. In equilateral prisms, the internal light path becomes symmetric at minimum deviation.

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