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A ray of light passes from a medium A having refractive index 1.6 to the medium B having refractive index 1.5. The value of the critical angle of medium A is ________.

Asked in GUJCET 2015 · Total internal reflection and optical fibres

• (1) sin⁻¹(1/(1.6))
• (2) sin⁻¹((16)/(15))
• (3) sin⁻¹(1/2)
• (4) sin⁻¹((15)/(16))

Step-by-step solution

Why the other options are wrong

• (1) comes from this is the critical angle of medium A measured against air. Here the light leaves A into B, so the rarer medium is B and sin C=(n_B)/(n_A)=(1.5)/(1.6), not 1/(1.6).
• (2) (16)/(15) is greater than 1, and no angle has a sine greater than 1 — the ratio has been written upside down. It is the rarer index over the denser one.
• (3) sin⁻¹(1/2)=30° is the critical angle of a medium of refractive index 2 against air; it uses neither 1.6 nor 1.5.

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