Question

When light passes from a more-dense to a less-dense medium—from glass to air, for example—the angle of refraction predicted by Snell's Law can be 90° or larger. In this case the light beam is actually reflected back into the denser medium. This phenomenon, called total internal reflection, is the principle behind fiber optics. Snell's Law is given below. sin(θ1) sin(θ2) = v1 v2 Set θ2 = 90° in Snell's Law and solve for θ1 to determine the critical angle of incidence at which total internal reflection begins to occur when light passes from diamond to air. (Note that the index of refraction from diamond to air is the reciprocal of the index from air to diamond. Round your answer to one decimal place.)

Answer 1

Answer:

$-20.3^{\circ}\ or\ 180+20.3=200.3^{\circ}$

Explanation:

$n_1$ = Refractive index of air = 1

$n_2$ = Refractive index of diamond = 2.41

$\theta_1$ = Angle in air

$\theta_2$ = Angle in diamond = 90° (TIR)

From Snell's law we have

$\dfrac{sin\theta_1}{sin\theta_2}=\dfrac{n_1}{n_2}\\\Rightarrow sin\theta_1=sin\theta_2\dfrac{n_1}{n_2}\\\Rightarrow \theta_1=sin^{-1}(sin\theta_2\dfrac{n_1}{n_2})\\\Rightarrow \theta_1=sin^{-1}(sin90\dfrac{1}{2.41})\\\Rightarrow \theta_1=-20.3^{\circ}\ or\ 180+20.3=200.3^{\circ}$

The angle will be $-20.3^{\circ}\ or\ 180+20.3=200.3^{\circ}$