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Question:

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?

Answer:

Let I1 and I2 be the intensity of the two light waves.

For monochromatic light waves, I1 = I2

If, Ø = Phase difference between the two waves

Then, their resultant intensities can be obtained by the relation:

Phase difference of the light is given by: 2¶/λ x Path Difference

When path difference = λ,

Phase difference, Ø = 2¶

∴ I' = 2I1 +2I1 = 4I1

Given, I’ = K

∴ I1 = K/4

When path difference = λ/3

Phase difference, ø = 2¶/3

Hence, resultant intensity is given by,

Using equation (1), we can write:

IR = I1 = K/4

Hence, the intensity of light with path difference of λ/3 is K/4 units.


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