Ray Optics

JEE Main level, numerical answer, medium

257 of 295

Question 257 of 295

A prism of refractive index n1{n}_{1} and another prism of refractive index n2{n}_{2} are stuck together (as shown in the figure). n1{n}_{1} and n2{n}_{2} depend on λ,\lambda , the wavelength of light, according to the relation n1=1.2+10.8×10−14λ2{n}_{1}=1.2+\dfrac{10.8\times {10}^{-14}}{{\lambda }^{2}} and n2=1.45+1.8×10−14λ2{n}_{2}=1.45+\dfrac{1.8\times {10}^{-14}}{{\lambda }^{2}}
The wavelength for which rays incident at any angle on the interface
BCBC pass through without bending at that interface will be ____ nm.nm.

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Answer: 600

For no bending, n1=n2{n}_{1}={n}_{2}
1.2+10.8×10−14λ2=1.45+1.8×10−4λ21.2+\dfrac{10.8\times {10}^{-14}}{{\lambda }^{2}}=1.45+\dfrac{1.8\times {10}^{-4}}{{\lambda }^{2}}
On solving,

9×10−14=25λ29\times {10}^{-14}=25{\lambda }^{2}
λ=6×10−7\lambda =6\times {10}^{-7}
λ=600nm\lambda =600nm

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