Question

A prism of refractive index \(n_1\) and another prism of refractive index \(n_2\) are stuck together (as shown in the figure). \(n_1\) and \(n_2\) depend on \(\lambda \), the wavelength of light, according to the relation

\(n_1=1.2+\dfrac{10.8\times 10^{-14}}{\lambda ^2}\) and \(n_2=1.45+\dfrac{1.8\times 10^{-14}}{\lambda ^2}\)

The wavelength for which rays incident at any angle on the interface \(\text{BC}\) pass through without bending at that interface will be _____ \(\text{nm}\)
.

Answer 1

Light will not bend at the interface when both media have same refracting index.

So, for no bending, $n_1=n_2$

$1.2+\frac{10.8\times {10}^{-14}}{{\lambda }^2}=1.45+\frac{1.8\times {10}^{-14}}{{\lambda }^2}$

On solving,

$9\times {10}^{-14}=0.25{\lambda }^2$

$\Rightarrow \lambda =\frac{3\times {10}^{-7}}{0.5}=6\times {10}^{-7}$

$\therefore \lambda =600\times {10}^{-9}\text{m}=600\text{nm}$