What are the wavelengths that get intensified in the reflected beam when a glass plate 0.40 micron thick with a refractive index of 1.50 is illuminated by white light?
The wavelengths that get intensified in the reflected beam are 4800 A and 5200 A.
Thin-Film Interference in Glass Plate
Thin Film Interference: Thin-film interference is a phenomenon that occurs when light waves reflect off the top and bottom surfaces of a thin film, causing interference patterns. In this case, we are dealing with a glass plate that is illuminated by white light.
Calculation for Intensified Wavelengths
When white light hits the glass plate at a normal incidence, certain wavelengths undergo constructive interference in the reflected beam. Constructive interference happens for wavelengths that satisfy the condition 2nt = mλ, where n is the refractive index, t is the thickness of the thin film, λ is the wavelength in the medium, and m is an integer (order of interference).
Given Parameters:
- Thickness of glass plate (t): 0.40 micron
- Refractive index of glass (n): 1.50
- Limits of visible spectrum:
- V (violet): 4000 A
- R (red): 7000 A
Calculation:
For a glass plate 0.40 microns thick with a refractive index of 1.50, we can calculate the wavelengths that would be intensified in the reflected beam by solving the constructive interference condition for the first order (m=1) for the given limits of the visible spectrum.
Using the formula 2nt = mλ, we substitute the values:
2 * 1.50 * 0.40 = 1 * λ
λ = 1.20 microns = 1200 nm = 12000 A
The wavelengths that fall within the visible spectrum limits and satisfy the constructive interference condition for the glass plate are 4800 A (blue) and 5200 A (cyan), making them the wavelengths intensified in the reflected beam.