Question

For grazing emergence of a ray in a prism, find out minimum possible values for angle of incidence (i) and angle of refraction (r₁) for commonly used glass prism.

Answer 1

i. At the point of emergence in prism, the ray travels from a denser medium into rarer.

Thus, if r₂ = sin^-1 \((\frac{1}{n})\) is the critical angle, the angle of emergence e = 90°. This is called grazing emergence.

ii. Angle of prism A is constant for a given prism and A = r₁ + r₂.

Hence the corresponding r₁ and i will have their minimum possible values.

iii. For commonly used glass prisms,

n = 1.5 (r₂)_max = sin^-1 \((\frac{1}{n})\) = sin^-1 \((\frac{1}{1.5})\) = 41.49°

iv. If, prism is symmetric (equilateral),

A = 60°

∴ r₁ = 60° – 41°49′ = 18°11′

∴ n = 1.5 = \(\frac{sin(i_{min})}{sin(18^\circ11')}\)

sin (i_min) = 1.5 × sin (18°11′)

∴ ii_min = 27°55′ ≅ 28°.