Question

A ray of light passes through four transparent media with refractive indices ${\mu }_1,{\mu }_2,{\mu }_3$ and ${\mu }_4$ as shown in the figure.The surfaces of all media are parallel.If the emergent ray CD is parallel to the incident ray AB, we must have:

• A. ${\mu }_1={\mu }_2$
• B. ${\mu }_2={\mu }_3$
• C. ${\mu }_3={\mu }_4$
• D. ${\mu }_1={\mu }_4$

Answer 1

The correct option is D ${\mu }_1={\mu }_4$

Applying Snell’s law for refraction from media $1$ to media $2$

${\mu }_1\sin i={\mu }_2\sin r_1$

Applying Snell’s law for refraction from media $2$ to media $3$

${\mu }_2\sin r_1={\mu }_3\sin r_2$

Applying Snell’s law for refraction from media $3$ to media $4$

${\mu }_3\sin r_2={\mu }_4\sin i$

Multiplying the three equations we get,

${\mu }_1{\mu }_2{\mu }_3\sin i\sin r_1\sin r_2={\mu }_2{\mu }_3{\mu }_4\sin r_1\sin r_2\sin i$

$\Rightarrow {\mu }_1={\mu }_4$

Hence the correct answer is option (D).