An interference is observed due to two coherent sources A and B separated by a distance 4 λ along Y-axis where λ is the wavelength of the light source used. A detector D is moved along the positive X-axis. Find the total number of maxima points are observed on the X-axis excluding the points x = 0 and x = ∞ ?

Step-by-step solution

To obtain maxima the path difference A D - B D = n λ A D - x n = n λ A D = n λ + x n ...(i) Form ∆ l e ABD, A D 2 = A B 2 + B D 2 n λ + x n 2 = 16 λ 2 + x n 2 n 2 λ 2 + x n 2 + 2 n λ x n = 16 λ 2 + x n 2 2 n λ x n = 16 - n 2 λ 2 x n = 16 - n 2 λ 2 n For n = 0 ⇒ x 0 = ∞ n = 1 ⇒ x 1 = 16 - 1 2 λ = 15 λ 2 = 7.5 λ n = 2 ⇒ x 2 = 16 - 1 2 λ = 12 λ 4 = 3 λ n = 3 ⇒ x 3 = 16 - 9 6 λ = 7 λ 6 n = 4 ⇒ x 4 = 16 - 16 2 × 4 λ = 0 So the total no. of maxima points observed are 3.