A parallel beam of light of wavelength 500 nm is incident normally on a slit of width d. If the distance between slit and screen is 0.6 m and distance of second order minimum from the centre of the screen is 6.0 mm, What is the width of the slit?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.1 mm
The minima occur when -
$d\sin θ=mλ$
where,
d = Width of the slit
θ = Angle of diffraction
m = order of minima
λ = wavelength of light
The angle θ for the second order minimum is -
$\tan θ=\frac{y_3}{L}=\frac{6×10^{-3}}{0.6}=0.01$
for small θ,
$\sin θ≃0.01$
$∴d×\sin θ=mλ$
$d×0.01=2×500×10^{-9}$
$⇒d=1cm$