A prism of refractive index n1 and another prism of refractive index n2 are stuck together (as shown in the figure). n1 and n2 depend on λ, the wavelength of light, according to the relation n1=1.2+(10.8 × 10-14/λ2) and n2=1.45+(1.8 × 10-14/λ2) The wavelength for which rays incident at any angle on the interface B C pass through without bending at that interface will be nm.

Question

A prism of refractive index n1 and another prism of refractive index n2 are stuck together (as shown in the figure). n1 and n2 depend on λ, the wavelength of light, according to the relation n1=1.2+(10.8 × 10-14/λ2) and n2=1.45+(1.8 × 10-14/λ2) The wavelength for which rays incident at any angle on the interface B C pass through without bending at that interface will be nm. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

For no bending, n1=n2 1.2+(10.8 × 10-14/λ2)=1.45+(1.8 × 10-4/λ2) On solving, 9 × 10-14=25 λ2 λ=6 × 10-7 λ=600 nm

For no bending, n1​=n2​ 1.2+λ210.8×10−14​=1.45+λ21.8×10−4​ On solving, 9×10−14=25λ2 λ=6×10−7 λ=600nm

For no bending, $n_{1} = n_{2}$
$1.2 + \frac{10.8 \times 1 0 ^{- 14}}{λ ^{2}} = 1.45 + \frac{1.8 \times 1 0 ^{- 4}}{λ ^{2}}$
On solving,
$9 \times 1 0^{- 14} = 25 λ^{2}$
$λ = 6 \times 1 0^{- 7}$
$λ = 600 nm$