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Question:

A single slit of width 0.1mm is illuminated by a parallel beam of light of wavelength 6000Å and diffraction bands are observed on a screen 0.5m from the slit. The distance of the third dark band from the central bright band is:

4.5mm

1.5mm

3mm

9mm

Solution:

The correct option is D 9mm
Minima for a single slit diffraction is given by:
→sinθ=mλ/a
→θ=sin⁻¹(3×6×10⁻⁷/0.1×10⁻³)
sinθ is very small →sinθ≈tanθ=y/0.5
→y=0.5×3×6×10⁻⁷/0.1×10⁻³
y=9mm
→y=9mm