Question

A mixture of light, consisting of wavelength 590nm and an unknown wavelength, illuminates Young’s double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data, the wavelength of the unknown light is

(a) 393.4nm 

(b) 885.0nm

(c) 442.5nm 

(d) 776.8nm

Answer 1

(c) : For interference, by Young’s double slits, the path difference xd/D= nλ for bright fringes and xd/D = (2n +1)λ/2 for getting dark fringes.

The central fringes when x = 0, coincide for all wavelengths.
The third fringe of λ₁ = 590nm coincides with the fourth bright fringe of unknown wavelength λ.

∴ xd/D = 3 × 590 nm = 4 × λnm
∴ λ = (3 × 590)/4 = 442.5nm.