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MHT CET 2024 (9 May, Shift 1) · Total Internal Reflection

Total Internal Reflection question from MHT CET 2024 (9 May, Shift 1)

Q16MHT CET 2024 · 9 MAY · SHIFT 1Medium

Total Internal Reflection

Velocity of light in diamond is (512)\left(\frac{5}{12}\right)th times that in air. Velocity of light in water is (34)\left(\frac{3}{4}\right)th times that in air. The angle of incidence of ray of light travelling from water to diamond is (angle of refraction (r)=30∘)[(r) = 30^\circ) [ Given →sin⁡30∘=12]\rightarrow \sin 30^\circ = \frac{1}{2}]

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Answer: (a)

  1. n=cvn = \frac{c}{v}: nd=125n_d = \frac{12}{5}, nw=43n_w = \frac{4}{3}.
  2. Water to diamond: nwsin⁡i=ndsin⁡rn_w \sin i = n_d \sin r.
  3. 43sin⁡i=125×12=65⇒sin⁡i=65×34=910\frac{4}{3}\sin i = \frac{12}{5}\times\frac{1}{2} = \frac{6}{5} \Rightarrow \sin i = \frac{6}{5}\times\frac{3}{4} = \frac{9}{10}.
  4. So the answer is (a) sin⁡−1(9/10)\sin^{-1}(9/10).
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