One side of an equilateral prism is painted by a transparent material of refractive index . The refractive index of prism is 1.6

Question

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 ______. [2026]

Smart Achievers · Accepted Answer

(4)

$1.6 \sin 60 ° = n_{2} \sin 90 °$

$n_{2} = 1.6 \times \frac{\sqrt{3}}{2} = \frac{8}{10} \sqrt{3} = \frac{4 \sqrt{3}}{5}$

Solution

Q.
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 ______. [2026]

1 $\frac{3 \sqrt{3}}{1.6}$

2 $\sqrt{3}$

3 $\frac{3.2}{\sqrt{3}}$

4 $\frac{4 \sqrt{3}}{5}$

Ans.
(4)

$1.6 \sin 60 ° = n_{2} \sin 90 °$

$n_{2} = 1.6 \times \frac{\sqrt{3}}{2} = \frac{8}{10} \sqrt{3} = \frac{4 \sqrt{3}}{5}$

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Solution

Q. One side of an equilateral prism is painted by a transparent material of refractive index n2. The refractive index of prism is 1.6. The minimum value of n2 required for total internal reflection from painted face is ______. [2026]

1 331.6

2 3

3 3.23

4 435

Ans. (4) 1.6sin60°=n2sin90° n2=1.6×32=8103=435