Question

Two transparent mediums of refractive indices ${\mu }_1$ and $m{u}_3$ have a solid lens shaped transparent material of refractive index ${\mu }_2$ between them as shown in figures. A ray traversing these mediums is also shown in the figures.

Column I, Column II and Column III represent different relationship among refractive index $\left(\mu \right)$, wavelength of light $\left(\lambda \right)$ and velocity of light (v) in 3 different media.

$\begin{array}{cccccc}& ColumnI& & ColumnII& & ColumnIII\\ \left(I\right)& {\mu }_1>{\mu }_2& \left(i\right)& {\lambda }_2>{\lambda }_3& \left(P\right)& v_2>v_1\\ \left(II\right)& {\mu }_3>{\mu }_2& \left(ii\right)& {\lambda }_1={\lambda }_3& \left(Q\right)& v_2=v_3\\ \left(III\right)& {\mu }_1>{\mu }_3& \left(iii\right)& {\lambda }_1<{\lambda }_2& \left(R\right)& v_3<v_2\\ \left(IV\right)& {\mu }_2>{\mu }_3& \left(iv\right)& {\lambda }_2<{\lambda }_3& \left(S\right)& v_1=v_3\end{array}$

Which of the combination is correct for figure 1?

• A. (II)(i)(Q)
• B. (IV)(iv)(Q)
• C. (I)(iii)(P)
• D. (IV)(i)(P)

Answer 1

The correct option is B (IV)(iv)(Q)

When ray passes undeflected $\Rightarrow$ Same refractive index.
Ray bends towards normal $\Rightarrow$ Rarer to denser
Ray bends away from normal $\Rightarrow$ Denser to rarer
Hence,
figure: 1 $\Rightarrow {\mu }_3={\mu }_2>{\mu }_1$
figure: 2 $\Rightarrow {\mu }_3<{\mu }_2<{\mu }_1$
figure: 3 $\Rightarrow {\mu }_3>{\mu }_2={\mu }_1$
Also, Velocity $\propto$ wavelength $\propto \frac{1}{Refractiveindex}$