A filtered mercury lamp produces green light at 546.1 nm with a linewidth of 0.05 nm. The...

A filtered mercury lamp produces green light at 546.1 nm with a linewidth of 0.05 nm. The light illuminates a double slit of spacing 0.1 mm. Determine the visibility of the fringes on a screen 1 m away, in the vicinity of the fringe of order m = 20. (See problem 1.) If the discharge lamp is replaced with a white light source and a filter of bandwidth 10 nm at 546 nm, how does the visibility change?

Figure 1

Problem 1

Show that the visibility of double-slit fringes in the mth order is given by

where λ is the average wavelength of the light and Δλ is its linewidth.