The cross section of a prism is a regular hexagon. A narrow beam of light strikes a face of the prism just below the midpoint ( M ) of the edge AB . The beam is parallel to the top and bottom faces of

Question

The cross section of a prism is a regular hexagon. A narrow beam of light strikes a face of the prism just below the midpoint $(M)$ of the edge AB . The beam is parallel to the top and bottom faces of the prism. Find the minimum value of refractive index of the material of the prism for which the emergent beam will be parallel to the incident beam. Take $13 = 3.60$

If your answer is x then write 10x ?

TestHub · Accepted Answer

For light beam to emerge parallel to the incident direction it must strike the face DE which is parallel to face AB . It means incident ray at M must go to E (or below it). Let side length of hexagon be b .

$MN = 3 b ME = (\frac{b}{2})^{2} + (3 b)^{2} = \frac{13}{2} b$

Using Snell's law $1. sin 3 0^{\circ} = μ . sin θ \Rightarrow \frac{1}{2} = μ \frac{1}{3} \Rightarrow μ = \frac{13}{2}$

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JEE Advanced (2028)