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For a right angled prism, ray 1 is the incident ray and ray 2 is the emergent ray, as shown in the figure. The refractive index of the prism is ________.

Asked in GSEB Board July 2018 · Total internal reflection and optical fibres

Figure: Total internal reflection and optical fibres
Answer: (4) √2

Step-by-step solution

Given: a right-angled prism whose other two angles are 45°. Ray 1 strikes the vertical face along its normal, and ray 2 leaves grazing along the sloping face.

Idea: a ray that comes out grazing the surface has been refracted through 90°, and that happens only when it meets the surface exactly at the critical angle.

Ray 1 enters without bending, so inside the glass it is still travelling horizontally.

The sloping face is tilted at 45°, so its normal is 45° from that horizontal ray: the angle of incidence inside is 45°.

Snell's law at the sloping face with the emergent ray grazing, so r=90°: n sin 45°=1×sin 90°

n=1/(sin 45°)=√2

So 45° is the critical angle of this glass, which is what makes 45° prisms such convenient reflectors.

Why the other options are wrong

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