A microscope slide is placed on top of an identical slide
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Waves Sound and Physical Optics · Waves Sound and Physical Optics
Problem
A microscope slide is placed on top of an identical slide, but a thin strand of hair at one end creates a narrow wedge-shaped air film between the glass surfaces. The wedge angle is small enough that, over the region examined, the air-film thickness can be approximated as t(x)=kx, where x is the distance from the contact line and k=1.5×10−4 (dimensionless when x is in metres and t in metres).
White light is incident perpendicularly, and the observer views the reflection at normal incidence. The refractive index of air is 1.00, and that of glass is 1.52.
Answer the following about the colored fringes that appear along the wedge.
(a) Derive an expression for the vacuum wavelength λm(x) that experiences constructive interference at position x, writing your result in terms of k, x, the order number m, and any necessary constants.
(b) Using the expression from part (a), obtain a formula for the spatial separation Δx between adjacent bright fringes of the same wavelength (for example, between two successive green maxima).
(c) For green light of 550nm, calculate the distance Δxgreen between adjacent bright green fringes.
(d) The observed pattern contains vivid color transitions rather than evenly spaced monochromatic fringes. Explain how the position-dependent mapping of λm(x) across the visible spectrum produces the familiar "rainbow" appearance of the wedge.