A single beam of coherent light ($\lambda$ = 633 nm)is incident on two glass slides,which are touching at one end and are separated by a 0.0240-mm thick sheet of paper on the other end.The slides are 6.5 cm long.The beam is split into two beams,with the first reflecting off the bottom surface of the top slide and the second reflecting of the top surface of the bottom slide.You may assume that all the beams are perfectly vertical and that they are perpendicular to both slides,i.e.,the slides are nearly parallel.Both beams recombine above the slides.How many bright bands are observed along the length of the slides?

Question

Quizplus · Accepted Answer

The path difference between the two beams is given by 2tcosθ, where t is the thickness of the paper, and θ is the angle of incidence. Since the slides are nearly parallel, we can assume θ is very small, and hence cosθ ≈ 1. Thus, the path difference is approximately 2t.

The condition for constructive interference is that the path difference is an integer multiple of the wavelength, i.e.,

2t = mλ

where m is an integer. Solving for m, we get

m = 2t/λ = 2(0.0240 mm)/(633 nm) ≈ 1

Therefore, we expect one bright band for each half-wavelength shift, or about 75 bright bands along the length of the slides. The correct answer is (C).

A Single Beam of Coherent Light λ\lambdaλ = 633 Nm)is Incident on Two Glass Slides,which Are Touching

A Single Beam of Coherent Light $\lambda$ = 633 Nm)is Incident on Two Glass Slides,which Are Touching