Light of wavelength 623.0 nm is incident on a narrow slit. The diffraction pattern is viewed on a screen 76.5 cm from the slit. The distance on the screen between the second order minimum and the central maximum is 1.11 cm. What is the width a of the slit in micrometers (μm) ?

wave length of light λ = 623 x 10⁻⁹ m.

Distance of screen D = 76.5 x 10⁻² m

width of slit = d

Distance on the screen between the second order minimum and the central maximum = 2 λ D / d

1.11 x 10⁻² = (2 x 623 x 10⁻⁹ x 76.5 x 10⁻²) / d

d = (2 x 623 x 10⁻⁹ x 76.5 x 10⁻²) / 1.11 x 10⁻²

= 85872.97 x 10⁻⁹

= 85.87297 x 10⁻⁶

= 85.87 μm

width a of the slit is = 85.87 μm