Answer to Question #124860 in Physics for Mukelo Madolo

Question

The triangular prism with apex angle flux=7o shown above has an index of refraction n=1.66. what is the smallest angle of incidence theta1 for which a light ray can emerge from the other side? Hint: Total internal reflection


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Answer 1

Look at the figure:

Start with the minimum angle of incidence 0° relative to the left surface of the prism. Then the incidence angle for the inner surface will be 7°. Calculate whether this is smaller than the critical angle for total internal refraction:

$$\theta_c=\text{arcsin}\frac{1}{1.66}=37°>7°.$$

Therefore, for the smallest angle of incidence 0° total internal refraction will not occur.

Apply Snell's law to calculate the angle of refraction:

$$\theta=\text{arcsin}\frac{\text{sin}7°}{1.66}=4°.$$