Optics 2 Question 11
11. 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 $C D$ is parallel to the incident ray $A B$, we must have
(2001, 2M)
(a) $\mu _1=\mu _2$
(b) $\mu _2=\mu _3$
(c) $\mu _3=\mu _4$
(d) $\mu _4=\mu _1$
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Answer:
Correct Answer: 11. (d)
Solution:
- Applying Snell’s law at $B$ and $C$, $\mu \sin i=$ constant or
$$ \mu _1 \sin i _B=\mu _4 \sin i _C $$
But $\quad A B || C D$
$$ \therefore \quad i _B=i _C $$
or
$$ \mu _1=\mu _4 $$
NOTE
The Snell’s law, which the
students read in their plus two syllabus $\mu=\frac{\sin i}{\sin r}$ is derived from $\mu \sin i=$ constant or $\mu _1 \sin i _1=\mu _2 \sin i _2$
Here : $\mu _1=1, \mu _2=\mu$, or $\sin i=\mu \sin r$ or $\mu=\frac{\sin i}{\sin r}$
