Question

In Young's double slit experiment, the two slits act as coherent sources of equal amplitude A and wavelength `lambda`. In another experiment with the same set up the two slits are of equal amplitude A and wavelength `lambda`. but are incoherent. The ratio of the intensity of light at the mid-point of the screen in the first case to that in the second case is ____________.

Options

• 1 : 2

• 2 : 1

• 4 : 1

• 1 : 1

Answer 1

In Young's double slit experiment, the two slits act as coherent sources of equal amplitude A and wavelength `lambda`. In another experiment with the same set up the two slits are of equal amplitude A and wavelength `lambda`. but are incoherent. The ratio of the intensity of light at the mid-point of the screen in the first case to that in the second case is 2 : 1.

Explanation:

Resultant intensity,

`"I" = "I"_1 + "I"_2 + 2 sqrt("I"_1 "I"_2) "cos" phi`

At central position with coherent source,

`"I"_"coh" = 4  "I"_0`      `(because "I"_1 = "I"_2 = "I"_0)`   ....(i)

`"In case of incoherent at a given point", phi  "varies randomly with time" Rightarrow ("cos" phi)_"av" = 0`

`therefore "I"_ "incoh" = "I"_1 + "I"_2 = 2  "I"_0`     ....(ii)

`therefore "I"_"coh"/"I"_"incoh" = 2/1`     ....[from (i) and (ii)]