Question

In Fig, CP represents a wave front and AO and BP are two rays corresponding to this wave front. The condition, for constructive interference, at P, between ray BP and ray OP, is

(1) cosθ = \(\frac{3λ}{2d}\)

(2) cosθ = \(\frac{λ}{4d}\)

(3) (secθ - cosθ) = \(\frac{λ}{d}\)

(4) (secθ - cosθ) = \(\frac{4λ}{d}\)

Answer 1

 (2) cosθ = \(\frac{λ}{4d}\)

From right angled triangle OPR,

Let Δ be the path difference, at P, between the two rays. Obviously

There is an additional path difference, λ/2 between the two rays due to reflection at the boundary of a denser medium. For constructive interference, at P, we, therefore, have