Q18DQ - University Physics with Modern Physics

Question

For the old “rabbit-ear” style TV antennas, it’s possible to alter the quality of reception considerably simply by changing the orientation of the antenna. Why?

Step-by-Step Solution

Answer

The critical angles are 38.12º  and 55.37º for glass-air and glass-water interface respectively.

Step 1: (a) Concept of critical angle.

 When light travels from a denser to the rarer medium, the angle of incidence in the denser medium for which the angle of refraction is 90º causing the refracted light to graze the boundary separating the two medium is known as the critical angle.

Step 2: (b) Explanation of the argument.

The refractive indices,

 $n_{glass}=1.62,n_{air}=1and n_{glass}=1.333$

Now,

The expression of critical angle is,

 ${\theta }_c=arc\sin \frac{n_1}{n_2}$

For glass-air interface,

$$\begin{gathered} {\theta }_c=arc\sin \frac{n_{air}}{n_{glass}} \\ =arc\sin \frac{1}{1.62} \\ =381.2 \end{gathered}$$

For glass-water interface,

$$\begin{gathered} {\theta }_c=arc\sin \frac{n_{water}}{n_{glass}} \\ =arc\sin \frac{1.333}{1.62} \\ =55.37 \end{gathered}$$

Thus, the critical angles are 38.12º   and 55.37º.