Question

When two coherent monochromatic light beams of intensities I and 4I are superimposed, then what are the maximum and minimum possible intensities in the resulting beams?

Options

• 5I and 4I

• 5I and 3I

• 9I and I

• 9I and 3I

Answer 1

9I and I

Explanation:

Given I₁ = 4I                I₂ = I

Maximum intensity I_max = `(sqrt"I"_1+sqrt"I"_2)^2`

I_max = `(sqrt(4"I")  +sqrt"I")^2`

= `(2sqrt"I"+sqrt"I")^2`

= `(3sqrt"I")^2`

= 9I

Minimum intensity I_min = `(sqrt"I"_1-sqrt"I"_2)^2`

I_min = `(sqrt(4"I")-sqrt"I")^2`

= `(2sqrt"I"-sqrt"I")^2`

= `(sqrt"I")^2`

= I