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

Numerical

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 K units. What is the intensity of light at a point where path difference is λ /3?

#### 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"_1"I"_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"_1"I"_1) cos phi

= 2"I"_1 + 2"I"_1 cos phi

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

Since path difference = λ,

Phase difference, phi = 2π

∴ I' = 2"I"_1 + 2"I"_1 = 4"I"_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"_1"I"_1) cos  (2pi)/3

= 2"I"_1 + 2"I"_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.

Concept: Interference of Light Waves and Young’S Experiment
Is there an error in this question or solution?

#### APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 10 Wave Optics
Q 5 | Page 383
NCERT Physics Part 1 and 2 Class 12
Chapter 10 Wave Optics
Exercise | Q 10.5 | Page 383