Fringe Width and Scaling
In the paraxial Young experiment, successive bright or dark fringes are separated by beta = lambda D/d. In a medium of refractive index mu, wavelength becomes lambda_0/mu and the fringe width decreases by the same factor.
Why this shows up in the exam
Wavelength comparison · Interferometer design · Refractive-index demonstrations
Learn the idea
YDSE fringe width grows with wavelength and screen distance but shrinks with slit separation and refractive index. Spread the screen farther and the same angular stripes separate more; move the slits farther apart and phase changes faster across the screen.
🧠 Memory hook: Lambda and D widen; d and mu tighten.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- beta = lambda D/d — linear fringe width in the small-angle regime
- Delta theta approximately lambda/d — angular fringe separation
- beta_medium = lambda₀ D/(mu d) — fringe width in a medium
How to approach it
- 1Use proportional reasoning before arithmetic
- 2Separate angular and linear quantities
- 3Check whether the apparatus is immersed or only a plate is inserted
Common slip-ups that cost marks
- •Making angular width depend on screen distance
- •Forgetting wavelength changes in a medium
- •Confusing fringe width with distance from the central fringe
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A real object is placed 30 cm from a converging lens of focal length 10 cm. Find the real image distance.
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