Question

Light of wavelength 450 nm falls on a 0.47 mm wide slit and forms a diffraction pattern on a screen 1.7 m away.

(a) Find the position of the first dark band on each side of the central maximum.

mm

(b) Find the width of the central maximum.

mm

Answer 1

given

lamda = 450 nm = 450*10^-9 m

d = 0.47 mm = 0.47*10^-3 m

R = 1.7 m

a) the position of the first dark band on each side of the central maximum,

y1 = lamda*R/d

= 450*10^-9*1.7/(0.47*10^-3)

= 1.63*10^-3 m

= 1.63 mm

b) the width of the central maximum, w = 2*lamda*R/d

= 2*450*10^-9*1.7/(0.47*10^-3)

= 3.26*10^-3 m

= 3.26 mm