JEE Main 2026 — Apr 2, Shift 2 — Physics solution

JEE Main2026Apr 2, Shift 2Physics

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
$\frac{4 3}{5}$

Solution

For an equilateral prism (all angles $6 0^{\circ}$ ), a ray entering normally on one face strikes the painted face at $6 0^{\circ}$ from the normal.

The condition for critical angle at the prism-paint interface: $n_{1} sin 6 0^{\circ} = n_{2} sin 9 0^{\circ}$ at the threshold.

So $n_{2} = 1.6 \cdot \frac{3}{2} = \frac{1.6 3}{2} = \frac{4 3}{5}$ .

For total internal reflection, $n_{2}$ must be at most this value (light goes from denser prism to rarer paint). The given expression is the threshold.

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