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  • A prism of refractive index and another prism of refractive index are stuck together (as shown in the figur

A prism of refractive index \mathrm{n}_{1} and another prism of refractive index \mathrm{n}_{2} are stuck together (as shown in the figure). \mathrm{n}_{1}$ and $\mathrm{n}_{2}depend on \lambda, the wavelength of light, according to the relation
\mathrm{n}_{1}=1.2+\frac{10.8 \times 10^{-14}}{\lambda^{2}}$ and $\mathrm{n}_{2}=1.45+\frac{1.8 \times 10^{-14}}{\lambda^{2}}
The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be ______nm.
 

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best_answer

If the rays incident at any angle on the interface BC passes through without bending at the interface.

\begin{aligned} &\therefore n_{1}=n_{2} \\ &1.2+\frac{10.8 \times 10^{-14}}{\lambda^{2}}=1.45+\frac{1.8 \times 10^{-14}}{\lambda^{2}} \end{aligned}

\begin{aligned} &\frac{9 \times 10^{-14}}{\lambda^{2}}=0.25 \\ &\lambda^{2}=\frac{9}{0.25} \times 10^{-14} \\ &\lambda=\frac{3}{0.5} \times 10^{-7} \\ &\lambda=600 \mathrm{~nm} \end{aligned}

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vishal kumar

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