Thin Film Interference
2nt cosθ_t = mλ — soap film, oil slick, anti-reflection coatings.
Key Notes
Light reflects from both the top and bottom surfaces of a thin film, producing interference between the two reflected beams.
Path difference between the two reflected rays: 2nt cos θ_t, where n = film index, t = film thickness, θ_t = angle inside the film.
When reflection occurs at a denser medium, the reflected wave undergoes a π phase shift (equivalent to extra λ/2 path).
Soap film in air (n_film > n_air, single denser-medium reflection at top): bright when 2nt cos θ_t = (m + ½)λ.
Anti-reflection coating on glass: film of index √n_glass, thickness λ/(4n_film) — destructive interference suppresses reflection at one wavelength.
The vivid colours of soap bubbles, oil slicks, and butterfly wings come from selective wavelength interference — thickness varies, so different colours appear at different places.
Newton's rings: a special thin-film geometry (plano-convex lens on flat glass) — concentric dark/bright rings centered on contact point.
Formulas
Path difference (general)
Geometric optical path difference between the two reflected rays inside the film.
Bright in reflection (one π-shift)
When only ONE of the reflections undergoes π phase shift (e.g., soap film in air).
Dark in reflection (one π-shift)
Destructive — same setup.
Anti-reflection coating
Minimum thickness for destructive interference at normal incidence (typical n_film = √n_glass).
Newton's rings (dark, in reflection)
Radius of m-th dark ring; R = radius of curvature of lens.
Important Points
Count the π-shifts: ZERO or TWO shifts → bright at 2nt cos θ_t = mλ, dark at (m+½)λ. ONE shift → reversed.
Anti-reflection coatings reduce reflectance by half for a single wavelength; broadband ARs use multilayer stacks.
Soap bubble thinned by evaporation: top becomes very thin (< λ/4n), almost no path difference, only the π shift remains → DARK — the bubble pops just after this region appears.
Thin-film interference requires film thickness comparable to λ; thicker films give too many overlapping fringes that wash out.
Newton's rings central spot is DARK in reflection (path diff ~0, but one π shift) — useful experimental check.
Thin Film Interference notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.