All Problems Interference of Light
Problem 5.73
A lens of diameter \(5.0 \mathrm{~cm}\) and focal length \(f=25.0 \mathrm{~cm}\) was cut along the diameter into two identical halves. In the process, the layer of the lens \(a=1.00 \mathrm{~mm}\) 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 \(\lambda=0.60 \mu \mathrm{m} .\) Behind the lens a screen was located at \(a\) distance \(b=50 \mathrm{~cm}\) 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 \(\delta_{\max }\) at which the fringes on the screen will be still observed sufficiently sharp.
5.73. (a) \(\Delta x=\lambda f / a=0.15 \mathrm{~mm}, 13\) maxima; (b) the fringes are still sufficiently sharp when \(\delta x \leqslant \Delta x / 2,\) where \(\delta x\) is the shift of the fringes from the extreme elements of the slit, hence, \(\delta_{\max }=\) \(=\lambda f^{2} / 2 a b=37 \mu \mathrm{m}\)