A prism is a triangular glass block that refracts (bends) light. In Class 12 Physics optics, you need to master two critical prism formulas.
Apex Angle (A): The top angle of the prism.
Minimum Deviation Formula: μ = sin[(A+δₘ)/2] / sin(A/2).
Dispersion: A prism disperses white light into its VIBGYOR spectrum.
Cause: Different wavelengths of light refract at different angles.
1. Angle of Deviation (δ) δ = (i₁ + i₂) – A Where: i₁ = angle of incidence, i₂ = angle of emergence, A = apex angle of prism.
2. At Minimum Deviation (δₘ) When the prism is at its minimum deviation, refraction is symmetric: i₁ = i₂ = i, and r₁ = r₂ = r = A/2 So: A + δₘ = 2i → i = (A + δₘ)/2
3. Refractive Index of Prism (μ) μ = sin[(A + δₘ)/2] / sin(A/2) This is the most important formula for the board exam.
Minimum deviation occurs when the refracted ray inside the prism travels parallel to the base. At this position, the angle of incidence equals the angle of emergence, and the deviation is at its smallest possible value.
μ = sin[(A + δₘ)/2] / sin(A/2), where A is the prism angle and δₘ is the angle of minimum deviation.
Minimum deviation is the condition where the refracted ray inside the prism is parallel to the base, and the angle of deviation is at its smallest value.
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