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Light enters at an angle of incidence in a transparent rod of refractive index μ. For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face whatsoever be the value of angle of incidence?

Asked in CBSE AIPMT 1998 · Total internal reflection and optical fibres

• (1) μ>√2
• (2) μ=1
• (3) μ=1.1
• (4) μ=1.3

Step-by-step solution

Why the other options are wrong

• (2) μ=1 is air, so there is no boundary to reflect at and the light is not guided at all
• (3) comes from at μ=1.1 a ray entering at grazing incidence refracts to r=sin⁻¹(1/(1.1))=65.4° and so meets the lateral face at only 24.6°, far short of the critical angle 65.4°, and escapes
• (4) comes from at μ=1.3 the same grazing ray refracts to 50.3° and meets the lateral face at 39.7°, still short of the critical angle 50.3°, so it escapes too

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