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  • The speed of light in media M1 and M2 is 1.5 x 108 m/s and 2.0 x 108 m/s respectively. A ray of light enters fr

The speed of light in media M1 and M2 is 1.5 x 108 m/s and 2.0 x 108 m/s respectively. A ray of light enters from medium M1 to M2 at an incidence angle i. If the ray suffers total internal reflection, the value of i is

Option: 1

Equal to \text{Sin}^{-1}\frac{2}{3}


Option: 2

Equal to or less than \text{Sin}^{-1}\frac{3}{5}


Option: 3

Equal to or greater than \text{Sin}^{-1}\frac{3}{4}


Option: 4

Less than \text{Sin}^{-1}\frac{2}{3}


Answers (1)

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\\ Given, \ v_{1}=1.5 \times 10^{8} \mathrm{m} / \mathrm{s}, \ v_{2}=2.0 \times 10^{8} \mathrm{m} / \mathrm{s}\\ \text{Refractive index for medium} \ M_{1} \ is \ \mu_{1}=\frac{c}{v_{1}}=\frac{3 \times 10^{8}}{1.5 \times 10^{8}}=2 \\ \text{Refractive index for medium} \ M_{2} \ is \mu_{2}=\frac{c}{v_{2}}=\frac{3 \times 10^{8}}{2.0 \times 10^{8}}=\frac{3}{2} \\ \text{If i is the angle of incidence and C is the critical angle then for total internal reflection} \\ \sin i \geq \sin C \\ But \ \sin C=\mu_{2} / \mu_{1} \\ \therefore \sin i \geq \frac{\mu_{2}}{\mu_{1}} \geq \frac{3 / 2}{2} \\or \ i \geq \sin ^{-1}\left(\frac{3}{4}\right)

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Anam Khan

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