Question

Two transparent media of refractive indices ${\mu }_1$ and ${\mu }_3$ have a solid lens shaped transparent material of refractive index ${\mu }_2$ between them as shown in figures in List 2. A ray traversing these media is also shown in the figures. In List 1 different relationships between ${\mu }_1,{\mu }_2$ and ${\mu }_3$ are given. Match them to the ray diagram shown in List 2.

Answer 1

In the above equation, as sine is an increasing function in $0$ to $\frac{\pi }{2}$, if ${\mu }_2>{\mu }_1,i>r$ and if ${\mu }_2<{\mu }_1,i<r$.
Thus light rays going from rarer medium to denser medium will bend towards the normal and vice versa.
It can be seen from the image how the light rays bend when they refract at a curved surface. (Line along the radius is the normal here as shown in the figure)
If the ray goes undeviated, then the refractive indexes are same.
So in 1, ${\mu }_1<{\mu }_2$ and ${\mu }_2={\mu }_3$
So in 2, ${\mu }_1>{\mu }_2$ and ${\mu }_2>{\mu }_3$
So in 3, ${\mu }_1<{\mu }_2$ and ${\mu }_2={\mu }_3$
So in 4, ${\mu }_1>{\mu }_2$ and ${\mu }_2>{\mu }_3$
So in 5, ${\mu }_1>{\mu }_2$ and ${\mu }_2={\mu }_3$