A ray incident on the solid at an angle of incidence equals to 5 3 ∘ on the vert | TestHub

Passage / Comprehension

Pulfrich refractometer is used to measure the refractive index of solids and liquid. It consist of right angled prism $A$ having its two faces perfectly plane. One of the face is horizontal and the other is vertical as shown in the figure. The solid $B$ whose refractive index is to be determined is taken having two faces cut perpendicular to one another. Light is incident in a direction parallel to the horizontal surface so that the light entering the prism $A$ is at critical angle $C$ . Finally, it emerges from the prism at an angle $i$ .\\

Let the refractive index of the solid be $μ$ and that of the prism $A$ be $μ_{0}$ (which is known). Here $μ_{0} > μ$ and by measuring $i$ , $μ$ can be determined.

A ray incident on the solid at an angle of incidence equals to $5 3^{\circ}$ on the vertical face of the solid. The ray just fail to emerge from the prism, if refractive index of prism is $3$ , then refractive index of the solid will be

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Solution:

At vertical face of solid: $sin 5 3^{\circ} = μ sin r$ , so $μ sin r = 0.8$

Just fails to emerge from prism: $3 cos r^{'} = 1$ , so $sin r^{'} = 2/3$

At solid-prism face: $μ cos r = 3 sin r^{'} = 2$

$μ^{2} = 0.64 + 2 = 2.64 = \frac{66}{25}$

$μ = \frac{66}{5}$

Physics - Geometrical Optics Question with Solution | TestHub

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