A diffraction pattern forms when light passes through a sing

A diffraction pattern forms when light passes through a single slit. The wavelength of the light is 587 nm. Determine the angle that locates the first dark fringe when the width of the slit is (a) 3.4 × 10-4 m and (b) 3.4 × 10-6 m.

Solution

1.

using diffraction equation:

m*lambda = d*sin A

sin A = m*lambda/d

A = arcsin (m*lambda/d)

given

lambda = 587*10^-9 m

d = 3.4*10^-4 m

m = 1

A = arcsin (587*10^-9/(3.4*10^-4))

A = 0.098919 deg

2.

using diffraction equation:

m*lambda = d*sin A

sin A = m*lambda/d

A = arcsin (m*lambda/d)

given

lambda = 587*10^-9 m

d = 3.4*10^-6 m

m = 1

A = arcsin (587*10^-9/(3.4*10^-6))

A = 9.9417 deg