Question

In Young’s double-slit experiment using monochromatic light ofwavelength λ, the intensity of light at a point on the screen wherepath difference is λ, is K units. What is the intensity of light at apoint where path difference is λ/3?

Answer 1

Let I 1 and I 2 be the intensities of two waves.

Let I ′ be the resultant intensity of the two waves

The resultant intensity is,

I ′ = I 1 + I 2 +2 I 1 I 2 cosϕ

Where ϕ is the phase difference between the two waves.

For monochromatic waves, I 1 = I 2

Phase difference is given as,

ϕ= 2π λ ×path difference

Since, path difference is λ

Thus,

ϕ= 2π λ ×λ =2π

Hence, resultant intensity is

I ′ = I 1 + I 1 +2 I 1 I 1 cos2π =2 I 1 +2 I 1 =4 I 1

Therefore,

4 I 1 =K

I 1 = K 4 (i)

Now, given path difference is λ 3

Phase difference is 2π 3

Therefore, resultant intensity is,

I ′ = I 1 + I 1 +2 I 1 I 1 cos 2π 3 =2 I 1 +2 I 1 ( − 1 2 ) = I 1

From equation (i), I 1 = K 4

Hence, the intensity of light at a point where path difference is λ 3 is K 4 .