Question 266: Ray Optics

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
$${n_1} = 1.2 + {{10.8 	imes {{10}^{ - 14}}} \over {{\lambda ^2}}}$$ and $${n_2} = 1.45 + {{1.8 	imes {{10}^{ - 14}}} \over {{\lambda ^2}}}$$
The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be _____________ nm.

Accepted Answer

For no bending, n
1
= n
2
$$1.2 + {{10.8 	imes {{10}^{ - 14}}} \over {{\lambda ^2}}}$$ = $$1.45 + {{1.8 	imes {{10}^{ - 14}}} \over {{\lambda ^2}}}$$
On solving,
9 $$	imes$$ 10
$$-$$14
= 25$$\lambda$$
2
$$\lambda$$ = 6 $$	imes$$ 10
$$-$$7
$$\lambda$$ = 600 nm

Ray Optics

Integer / Numeric Answer Type