Young's double-slit experiment shows that light can behave like a wave by producing a pattern of bright and dark bands called interference fringes. A coherent light source shines through two very narrow slits, and the overlapping waves spread out toward a screen. Where the waves arrive in step, they make a bright fringe, and where they arrive out of step, they make a dark fringe.
This experiment matters because it gives direct evidence that light has wavelength and phase, not just particle-like motion.
Key Facts
- Path difference between the two slits controls interference: Δr = r2 - r1.
- Bright fringes occur when Δr = mλ, where m = 0, 1, 2, 3, ...
- Dark fringes occur when Δr = (m + 1/2)λ, where m = 0, 1, 2, 3, ...
- For small angles, fringe position on the screen is y = mλL/d for bright fringes.
- Fringe spacing is Δy = λL/d, where L is screen distance and d is slit separation.
- Increasing wavelength or screen distance spreads fringes farther apart, while increasing slit separation makes fringes closer together.
Vocabulary
- Coherent light
- Light waves are coherent when they maintain a constant phase relationship and usually have the same frequency.
- Interference
- Interference is the combination of overlapping waves that can produce larger or smaller total amplitudes.
- Constructive interference
- Constructive interference occurs when waves meet in phase and reinforce each other to make a bright fringe.
- Destructive interference
- Destructive interference occurs when waves meet out of phase and cancel to make a dark fringe.
- Path difference
- Path difference is the difference in distance traveled by waves from the two slits to the same point on the screen.
Common Mistakes to Avoid
- Using the slit width instead of the slit separation in y = mλL/d is wrong because d is the distance between the centers of the two slits, not the width of one slit.
- Forgetting to convert nanometers to meters is wrong because all quantities in the interference equations must use consistent units.
- Counting the central bright fringe as m = 1 is wrong because the central maximum has zero path difference and is labeled m = 0.
- Assuming dark fringes occur at Δr = mλ is wrong because that condition gives constructive interference, while dark fringes occur at half-integer multiples of the wavelength.
Practice Questions
- 1 A double-slit setup uses light with wavelength 600 nm, slit separation 0.20 mm, and screen distance 2.0 m. What is the distance from the central bright fringe to the first-order bright fringe?
- 2 In a double-slit experiment, adjacent bright fringes are spaced 4.5 mm apart on a screen 1.5 m away. If the slit separation is 0.25 mm, what is the wavelength of the light?
- 3 If the slit separation is increased while the wavelength and screen distance stay the same, what happens to the spacing between bright fringes? Explain using the fringe spacing equation.