Question

light of wavelength 580 nm is incident on a slit of width 5.47 x 10^-6m. An observing screen is placed 2.00 m from the slit. A) Find he position of the first order dark fringe from the center of the screen (in meters) B) At most, how many dark fringes can be formed on either side of the central bright fringe (assuming that the observing screen is infinitely long)?

Answer 1

Here ,

slit width , d = 5.47 *10^-6 m

wavelength = 580 nm

screen distance , D = 2 m

a)for the first dark fringe

y = m * wavelength *D/d

y = 1*580 *10^-9 * 2/(5.47 *10^-6)

y = 0.212 m

the first dark fringe is 0.212 m from the centre

b)

let the order of fringes is n

d * sin(theta) = n * lamda

5.47 *10^-6 * sin(90) = n * 580 *10^-9

n = 9.43 = 9

total number of dark fringes seen = 9 * 2

total number of dark fringes seen = 18

the total number of dark fringes seen is 18