Question

In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index ‘n‘. For incident angle 60° at the side AC the refracted light beam just grazes along face AC. The refractive index of the liquid n = $(\sqrt x)/4$. The value of $x$ is _______.(Given refractive index of glass = $1.5$)

Answer 1

$1.5 \;sin60° = 4 \;sin90°$

$1.5×\frac{\sqrt3}{2}$

=$\frac{3\sqrt3}{4}$

=$\frac{\sqrt{27}}{4}$

=$\frac{x}{4}$

$x = 27$