Question

A slit or an aperture diffracts light. Even then we say light travels in a straight line and ray optics is valid. Comment.

Answer 1

A slit of width a diffracts a beam of light. Half angular width of central maximum is:

θ ≅ sin θ = \(\frac{\lambda}{a}\) 

In travelling distance z, half angular width of beam would become \((\frac{z\lambda}{a})\) 

This width will become more than width of slit, i.e. \(\frac{z\lambda}{a} > a,\)

where z > \(\frac{a^2}{\lambda}\)

We call \(\frac{a^2}{\lambda}\) = z_F, Fresnel distance.

Now, for a = 3 mm = 3 x 10^-3 m

λ = 5000 Å = 5 x 10^-7 m

z_F = \(\frac{a^2}{\lambda}\) = \(\frac{(3 \times 10^{-3})^2}{5 \times 10^{-7}}\) = 18 m

This means width of beam due to diffraction remains equal to the size of the width of the slit (3 x 10^-3) i.e. diffraction effect can be neglected (upto 18 m) and ray optics is valid.