A beam of light of wavelength 600 nm is incident along the normal to two closely spaced parallel glass plates.For what air gap separation between the plates will the transmitted beam be of maximum intensity? (1 nm = 10−⁹ m)

Question

Quizplus · Accepted Answer

When a beam of light is incident on two parallel plates, some of it is reflected and some is transmitted. The transmitted beam is constructively or destructively reinforced depending on the path difference between the two beams.
 
For constructive interference of the transmitted beam, the path difference between the two beams should be equal to an integer multiple of the wavelength of the light. Mathematically,

2d cosθ = mλ,

where d is the thickness of the glass plates, θ is the angle of incidence (which is zero in this case as the beam is incident along the normal), m is an integer, and λ is the wavelength of light.

Since m=0 for maximum intensity, we have:

2d cosθ = 0

or

2d = nλ,

where n = 1 (since the light is passing from air to glass) and λ = 600 nm.

Therefore, d = λ/2 = 300 nm.

Hence, the air gap separation between the plates for the maximum intensity of the transmitted beam is 300 nm.

A Beam of Light of Wavelength 600 Nm Is Incident