Advertisement Remove all ads

In Young'S Double Slit Experiment, Find Out the Intensity of Light at a Point Where Path Difference is λ/3 - Physics

In Young's double slit experiment, using monochromatic light of wavelength λ, the intensity of light at a point on the screen where path difference is λ, is K units. Find out the intensity of light at a point where path difference is λ/3.

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

Advertisement Remove all ads

Solution 1

Phase difference = `(2pi)/lambda` × Path difference 

ϕ1 =`(2pi)/lambda` × λ = 2π 

where ϕ1 is the phase difference when the path difference is λ and the corresonding frequency is I1=K

`phi_2=(2pi)/lambdaxxlambda/3=(2pi)/3`

where ϕ2 is the phase difference when the path difference is the `lambda/3` and the corresponding frequency is I2 
Using equation (iv), we get:

`I_1/I_2=(4a^2cos^2(phi_1/2))/(4a^2cos^2(phi_2/2))=(cos^2((2pi)/2))/cos^2(((2pi)/3)/2)=(cos^2(ph))/cos^2(pi/3)=1/(1/(2^2))=4`

`K/I_2=4`

`I_2=K/4`

Solution 2

Let I1 and I2 be the intensity of the two light waves. Their resultant intensities can be obtained as:

`I' = I_1 +` I_2 + 2sqrt(I_1I_2) cos phi`

Where,

`phi` = Phase difference between the two waves

For monochromatic light waves,

`I_1 = I_2`

`:. I' = I_1 + I_1 + 2sqrt(I_1I_1) cos phi`

`= 2I_1 + 2I_1 cos phi`

Phase difference = `(2pi)/lambda xx "Path diffrence"`

Since path difference = λ,

Phase difference, `phi = 2pi`

`:. I' = 2I_1  + 2I_1 = 4I_1`

Given

I’ = K

`:. I_1 = K/4`    ....(1)

When path difference= `pi/3`

Phase difference, `phi = (2pi)/3`

Hence, resultant intensity,  `i'_R = I_1 + I_1 + 2sqrt(I_1I_1) cos  (2pi)/3`

`= 2I_1 + 2I_1(-1/2) = I_1`

Using equation (1), we can write:

`I_R = I_1 = K/4`

Hence, the intensity of light at a point where the path difference is `pi/3  is K/4` units

  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×