4.5 Diffraction of Light

4.5 Diffraction of Light

Definition:

Diffraction is the bending of light waves around obstacles or through openings, causing the light to spread out. The extent of diffraction increases with increasing wavelength and decreasing size of the obstacle or aperture.

Single-Slit Diffraction:

When light passes through a single narrow slit, it spreads out and creates a diffraction pattern with a central bright fringe and successive dark and bright fringes on either side. The angle θ at which dark fringes occur is given by:
sin θ = mλ / a
where:
- m is the order of the dark fringe (m = ±1, ±2, ...),
- λ is the wavelength of light,
- a is the width of the slit.

Example Problem:

Calculate the angle of the first dark fringe in a single-slit diffraction pattern for light of wavelength 500 nm passing through a slit of width 0.1 mm.

Solution:

Using the formula for diffraction:
sin θ = (1 × 500 × 10⁻⁹ m) / (0.1 × 10⁻³ m) = 0.005
θ = arcsin(0.005) ≈ 0.29°
The angle of the first dark fringe is approximately 0.29 degrees.