Question

A monochromatic light with a wavelength lambda=600nm passes through a single slit which has a width of 0.800mm.

a.) What is the distance between the slit and the if the first minimum in the diffraction pattern is at a distance 1.00mm from the center of the screen?

b.) Calculate the width of the central maximum.

Please show all work and explain the concepts behind this if you can.

Answer 1

lamda = 600 nm
d = 0.8 mm = 0.0008 m
y1 = 1.00 mm = 0.001 m
a) let L is the distance between the slit and screen

for first minimum, y1 = lamda*L/d

L = y1*d/lamda

= 0.001*0.0008/(600*10^-9)

= 1.33 m

b) width of the central maximum, delta_y = 2*lamda*L/d

= 2*600*10^-9*1.33/0.0008

= 0.00200 m

= 2.00 mm