Question

Interference fringes are produced on a screen by using two light sources of intensities I and 9I. The phase difference between the beams is `pi/2` at point P and π at point Q on the screen. The difference between the resultant intensities at point P and Q is ______.

Options

• 2I

• 4I

• 6I

• 8I

Answer 1

Interference fringes are produced on a screen by using two light sources of intensities I and 9I. The phase difference between the beams is `pi/2` at point P and π at point Q on the screen. The difference between the resultant intensities at point P and Q is 6I.

Explanation:

Resultant intensity of interferring wave at 'P'.

I_p = I₁ + I₂ + 2`sqrt("I"_1"I"_2cosphi)`

For `phi=pi/2`

I_p = I + 9I = 10I

Again resultant intensity at 'Q'

I_Q =  I₁ + I₂ + 2`sqrt("I"_1"I"_2cosphi)`

For Φ = π, = I_Q = I + 9I +`(-2sqrt(9"I"^2))`

= 10I - 6I = 4I

∴ Difference between the resultant intensity

ΔI = I_p - I_Q 

= 10I - 4I = 6I