Question

A ray of light passes through four transparent media with refractive index $n_1,n_2,n_3$ and $n_4$ as shown. The surfaces of all media are parallel.
If the emergent ray $DE$ is parallel to the incident ray $AB$, then:

• A. $n_1=n_4$
• B. $n_2=n_4$
• C. $n_3=n_4$
• D. $n_1=\frac{n_2+n_3+n_4}{3}$

Answer 1

The correct option is A $n_1=n_4$

As the emergent ray $DE$ is parallel to incident ray $AB$, thus angle of incidence $i$ is equal to angle of refraction $r$.

$⟹$ $i=r$ ...........(1)

Using Snell's law of refraction,

$n_1\sin i=n_4\sin r$

$\therefore$ $n_1\sin i=n_4\sin i$ (using 1)

$⟹n_1=n_4$