Question

In an interference experiment, the ratio of amplitudes of coherent waves is `a_1/a_2 = 1/3.` The ratio of maximum and minimum intensities of fringes will be ______.

Options

• 2

• 18

• 4

• 9

Answer 1

In an interference experiment, the ratio of amplitudes of coherent waves is `a_1/a_2 = 1/3.` The ratio of maximum and minimum intensities of fringes will be 4.

Explanation:

Given: The amplitude ratio of two interfering waves is

`a_1/a_2 = 1/3` .......(i)

To find: `I_max/I_min`, the ratio of the maximum and minimum intensities of the interference pattern's fringes.

Let I₁ be the intensity that corresponds to amplitude a₁, and I₂ be the intensity that corresponds to amplitude a₂.

The maximum to minimum intensity ratio in the interference pattern will then be:

`I_max/I_min = (sqrtI_1 + sqrtI_2)^2/(sqrtI_1 - sqrtI_2)^2 = (I_1 + I_2 + 2sqrt(I_1I_2))/(I_1 + I_2 - 2sqrt(I_1I_2))`

Because the intensity is proportional to the square of the amplitude, putting `I_1 = a_1^2, I_2 = a_2^2.`

`I_max/I_min = (a_1^2 + a_2^2 + 2a_1a_2)/(a_1^2 + a_2^2 - 2a_1a_2)`

Now, putting a₂ = 3a₁,

`I_max/I_min = (16a_1^2)/(4a_1^2) = 4/1 = 4 : 1`