In a Young's double slit experiment using monochromatic light of wavelengths λ , the intensity of light at a point on the screen with a path difference λ is M units and the intensity of light at a point where the path difference is λ 3 is n M units. What is the value of n ?

Step-by-step solution

Resultant intensity I R = I 1 + I 2 + 2 I 1 I 2 c o s θ If path difference, = λ then phase difference = 2 π … . ∵ ϕ = 2 π λ × Δ x ∴ I R = I + I + 2 I × I c o s 2 π … . . ( ∵ I 1 = I 2 = I ) = 4 I = M If path difference = λ 3 then phase difference = 2 π λ × λ 3 = 2 π 3 rad I R ' = I + I + 2 I × I c o s 2 π 3 = 2 I + 2 I - 1 2 = I = M 4 = 0.25 M