Question

A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength 5 x 10⁻⁵ cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is
(1) 0.10 cm
(2) 0.25 cm
(3) 0.20 cm
(4) 0.15 cm

Answer 1

The distance of the first dark band of the diffraction pattern from the centre of the screen is y = 0.15 cm

Option (4) is correct.

Explanation:

Focal length "f" = D =  60 cm  

Beam of wavelength " λ" = 5 x 10⁻⁵ cm

For first minima:

y = λD / a = 5 × 10^−7 × 60 / 2 × 10^−2 × 10−2

y = 5 × 10^−3 x 60 / 2

y = 0.15 cm

Hence the distance of the first dark band of the diffraction pattern from the centre of the screen is y = 0.15 cm