Question

Two sources of intensity I and 41 are used in an interference experiment. Find the intensity at points where the waves from two sources superimpose with a phase

(i) Zero 

(ii) \(\frac{π}{2}\)

(iii) π

Answer 1

The resultant intensity at a point where phase difference is Φ is

I_R +I₁ + I₂ 2  +\(\sqrt{I_1I_2}\) cos Φ 

As I₁ + I and I₂ = 4I, therefore, 

I_R = I + 4I + 2 \(\sqrt{I. 4I}\) cos Φ 

I_R = 5I + 4I cos Φ

(i) When Φ = 0 ; I_R = 5I + 4I cos 0 = 9I 

(ii) When Φ =\(\frac{π}{2}\) ; I_R = 5I + 4I cos \(\frac{π}{2}\) = 5I 

(iii) When Φ = π ; I_R = 5I + 4I cos π = 51 – 41 = I 

Φ = 0 ; I_R = 9I 

Φ = \(\frac{π}{2}\) ; I_R = 5I 

Φ = π ; I_R = I