Question 34.4: Light Passing Through a Slab A light beam passes from medium...
Light Passing Through a Slab
A light beam passes from medium 1 to medium 2, with the latter medium being a thick slab of material whose index of refraction is n_2 (Fig. 34.14). Show that the beam emerging into medium 1 from the other side is parallel to the incident beam.
Conceptualize Follow the path of the light beam as it enters and exits the slab of material in Figure 34.14, where we have assumed that n_2 \gt n_1. The ray bends toward the normal upon entering and away from the normal upon leaving.
Categorize Like Example 34.3, this is another typical problem in which we apply the wave under refraction model.
Analyze Apply Snell’s law of refraction to the upper surface:
(1) \sin \theta_2=\frac{n_1}{n_2} \sin \theta_1
Apply Snell’s law to the lower surface:
(2) \sin \theta_3=\frac{n_2}{n_1} \sin \theta_2
Substitute Equation (1) into Equation (2):
\sin \theta_3=\frac{n_2}{n_1}\left(\frac{n_1}{n_2} \sin \theta_1\right)=\sin \theta_1Finalize Therefore, \theta_3=\theta_1 and the slab does not alter the direction of the beam. It does, however, offset the beam parallel to itself by the distance d shown in Figure 34.14.