One side of an equilateral prism is painted by a transparent material of refractive index $\mathrm{n}_{2}$. The refractive index of prism is 1.6. The minimum value of $\mathrm{n}_{2}$ required for total internal reflection from painted face is $\_\_\_\_$.

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Geometrical Optics

One side of an equilateral prism is painted by a transparent material of refractive index

n_{2}

. The refractive index of prism is 1.6. The minimum value of

n_{2}

required for total internal reflection from painted face is

____

(A) $\frac{3 3}{1.6}$
(B) $3$
(C) $\frac{3.2}{3}$
(D) $\frac{4 3}{5}$ ✓ Correct

Answer: (D)

Solution

The ray enters normally through one face and travels undeviated to the painted face; from the geometry of the equilateral prism it strikes that face at

6 0^{\circ}

. Total internal reflection occurs while this angle exceeds the critical angle

θ_{c}

, where

sin θ_{c} = \frac{n _{2}}{n _{p r i s m}}

. The limiting case is

θ_{c} = 6 0^{\circ}

, giving

n_{2} = n_{p r i s m} sin 6 0^{\circ} = 1.6 \times \frac{3}{2} = 0.8 3

. The limiting refractive index of the coating is

\frac{4 3}{5}

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Single correct option

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JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Geometrical Optics

Solution

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