Question 391: Ray Optics

Question

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

Accepted Answer

Refractive index for medium M
1
is
$$\mu $$
1
= $${{3 	imes {{10}^8}} \over {1.5 	imes {{10}^8}}}$$ = 2
Refractive index for medium M
2
is
$$\mu $$
2
= $${{3 	imes {{10}^8}} \over {2.0 	imes {{10}^8}}}$$ = $${3 \over 2}$$
For total internal reflection, sini $$ \ge $$ sinC
But sinC = $${{{\mu _2}} \over {{\mu _1}}}$$
sini $$ \ge $$ $${{{\mu _2}} \over {{\mu _1}}}$$ $$ \ge $$ $${{3/2} \over 2}$$
$$ \Rightarrow $$ i $$ \ge $$ sin
$$-$$1
$$\left( {{3 \over 4}} ight)$$

Answer

Equal to sin$$-$$1 $$\left( {{2 \over 3}} \right)$$

Answer

Equal to or less than sin$$-$$1$$\left( {{3 \over 5}} \right)$$

Answer

Equal to or greater than sin$$-$$1 $$\left( {{3 \over 4}} \right)$$

Answer

Less than sin$$-$$1$$\left( {{2 \over 3}} \right)$$

Ray Optics

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

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