Angular width of the central maxima in the Fraunhoffer diffraction for λ=6000 A is θ₀. When the same slit is illuminated by another monochromatic light, the angular width decreases by 30%. The wavelength of this light is

Question

Accepted Answer

(2) 4200 A. Given: at λ₁=6000 A the angular width is θ₀; a second wavelength narrows it by 30%, with the same slit. Idea: the angular width of the central maximum is 2θ=(2λ)/a, so at fixed slit width it is proportional to the wavelength. A decrease of 30% leaves (100-30)/(100)=0.70 of the original width. (θ₀)/(0.70 θ₀)=(λ₁)/(λ₂). λ₂=0.70×λ₁=0.70×6000. =4200 A.

Angular width of the central maxima in the Fraunhoffer diffraction for λ=6000 A is θ₀. When the same slit is illuminated by another monochromatic light, the angular width decreases by 30%. The wavelength of this light is

Step-by-step solution

Why the other options are wrong