Question

Red light of wavelength 675 nm is incident on a slit of width 4.56 × 10−6 m. An observing screen is placed 1.50 m from the slit.

9a) Find the distance between the third order dark fringe and the central bright fringe (in meters).

9b) If you replaced the single slit with two slits centered on the former position of the single slit, what would the separation between the two slits need to be in order for the second order bright fringe of the double-slit interference pattern to fall on the third order dark fringe of the single slit diffraction pattern?

9c) If the average adult pupil diameter is 3.5 mm, what distance from the observing screen is a person no longer able to resolve (distinguish) the second order bright fringe and the central bright fringe in the double slit interference pattern?

Answer 1

9a) lamda = 675 nm
a = 4.56*10^-6 m
L = 1.50 m
the distance between the third order dark fringe and the central bright fringe,
y3 = 3*lamda*L/a

= 3*675*10^-9*1.5/(4.56*10^-6)

= 0.666 m <<<<<<<<<<<-----------------------Answer

9b) let d is the slit separation.

for 3rd rark fringe, y3 = (2.5)*lamda*L/d

d = 2.5*lamda*L/y3

d = 2.5*675*10^-9*1.50/0.666

= 3.80*10^-6 m <<<<<<<<<<<-----------------------Answer

9c) minimum angular separtion to resolve, theta = 1.22*lamda/d

= 1.22*675*10^-9/(3.5*10^-3)

= 2.35*10^-4 radians

distance between central bright fringe and 2nd bright fringe, y2 = 2*lamda*L/d

= 2*675*10^-9*1.5/(3.8*10^-6)

= 0.5329 m
let r is the minimum distance between the person and the screen.

use, y2 = r*theta

r = y2/theta

= 0.5329/(2.35*10^-4)

= 2267 m <<<<<<<<<<<-----------------------Answer