Question

As shown in the figure, a parallel beam emerges parallel. The relation between $\mu ,{\mu }_1$and ${\mu }_2$ is:

• A. $\mu ={\mu }_1$+ ${\mu }_2$
• B. $\frac{1}{\mu }=\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2}$
• C. $\mu =\frac{{\mu }_1+{\mu }_2}{2}$
• D. $\frac{2}{\mu }=\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2}$

Answer 1

Answer: (D)

$\frac{2}{\mu }=\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2}$

We have
$t\propto \mu$

Since the rays of light on the left side is passing through a material of refractive index $\mu$ and right side through materials with refractive indices ${\mu }_1$ and ${\mu }_2$ we can write:

$\frac{t}{\mu }=\frac{\frac{t}{2}}{{\mu }_1}+\frac{\frac{t}{2}}{{\mu }_2}$

$⟹\frac{2}{\mu }=\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2}$