Interference & Diffraction

When light waves pass through two narrow slits, each slit sends out spreading waves that overlap on a screen behind them. Where a crest from one slit meets a crest from the other, they add up into a bright fringe; where a crest meets a trough, they cancel into a dark gap. Bright fringes only show up at the special angles where the extra distance one wave travels is a whole number of wavelengths.

d · sin θ = m · λ

• d — slit spacing (m): distance between the two slits (or lines on a grating)
• θ — angle (°): angle from the center of the pattern out to a bright fringe
• m — order number (unitless): which bright fringe it is, counting 0, 1, 2… out from the center
• λ — wavelength (m): the length of one full wave cycle of the light

Light of wavelength 500 nanometers shines through two slits spaced 20 micrometers apart. What is sin θ for the second bright fringe (m = 2)?

• d = 20 μm
• λ = 500 nm
• m = 2

1. sin θ = m · λ / d
2. sin θ = (2 × 500 nm) / 20 000 nm

sin θ = 0.05

Same slits (d = 20 micrometers) and same light (500 nanometers) — what is sin θ for the first bright fringe, m = 1?

• 0.025
• 0.05
• 0.1

If you slide the two slits farther apart (increase d) while keeping the wavelength and order the same, what happens to the fringe spacing?

• Spacing increases
• Spacing decreases
• Spacing stays the same