Question

Light of wavelength 650 nm is incident on a long, narrow slit. Find the angle of the first diffraction minimum for each of the following widths of the slit

(a) 1 mm

............rad

(b) 0.1 mm

...........rad

(c) 0.01 mm

..........rad

Answer 1

Wavelength, = 650 x 10^-9 m

Condition for first diffraction minimum:

sin = / a

(a)

Width of slit, a1 = 1 mm

                         = 1 x 10^-3 m

1 = sin^-1( 650 x 10^-9 / 1 x 10^-3 )

     = 1.13 x 10^-5 rad

(b)

Width of slit, a1 = 0.1 mm

                         = 1 x 10^-4 m

1 = sin^-1( 650 x 10^-9 / 1 x 10^-4 )

     = 1.65 x 10^-5 rad

Ans:

c)

Width of slit, a1 = 0.01 mm

                         = 1 x 10^-5 m

1 = sin^-1( 650 x 10^-9 / 1 x 10^-5 )

     = 1.66 x 10^-3rad