Question

A lens of diameter 5.0 cm and focal length f = 25.0 cm was cut along the diameter into two identical halves. In the process, the layer of the lens a = 1.00 mm in thickness was lost. Then the halves were put together to form a composite lens. In this focal plane a narrow slit was placed, emitting monochromatic light with wavelength λ = 0.60 μm. Behind the lens a screen was located at a distance b = 50 cm from it. Find:

(a) the width of a fringe on the screen and the number of possible maxima;

(b) the maximum width of the slit δmax at which the fringes on the screen will be still observed sufficiently sharp.

Answer 1

(a) We show the upper half oi the lens. The emergent light is at an angle a/2f from the axis.

Thus the divergence angle of the two incident light beams is

When they interfere the fringes produced have a width

The patch on the screen illuminated by both light has a width b ψ and this contains

(b) We follow the logic of (5.71 c). From one edge of the slit to the other edge the distance is of magnitude

If we imagine the edge to shift by this distance, the angle

and the light will shift

The fringe pattern will therefore shift by