Question

With a monochromatic light of wavelength ?? = 532 nm A double-slit interference pattern is produced on a screen as shown in the picture. The slit separation ?? is 0.10 mm, and the slit–screen separation ?? is 50 cm. Assume that the angle θ (from the slit center to the maxima and minima) small enough to permit use of the approximations sin θ ≈ tan θ ≈ θ, in which θ is expressed in radian measure.

a. A strip of transparent material of thickness ?? = 1.2 μm with index of refraction ?? =1.50 is placed over one of the slits. Its presence changes the interference between light waves from the two slits, causing the interference pattern to be shifted across the screen from the original pattern. Calculate the shifted position of the 1st minima.

b. Suppose we do not know the thickness of the transparent material and our goal is to determine its thickness such that the lower ?? = 1 bright fringe is shifted to the center of the pattern. Should the plastic be placed over the top slit (as arbitrarily drawn in the figure below) or the bottom slit, and what thickness ?? should it have?

Answer 1