A thin sheet of plastic (n = 1.60)is inserted between two panes of glass to reduce infrared ($\lambda$ = 700 nm)losses.What thickness (in nm)is necessary to produce constructive interference in the reflected infrared radiation?
A)218
B)109
C)55
D)318
E)443

Question

Quizplus · Accepted Answer

Constructive interference occurs when the optical path difference is an integer multiple of the wavelength. For a thin film, this condition is met when 2nt = mλ, where n is the refractive index, t is the thickness, and λ is the wavelength. Solving for t with m=1 gives t = λ/(2n) = 700 nm / (2 * 1.60) = 109 nm.

A Thin Sheet of Plastic (N = 1 λ\lambdaλ = 700 Nm)losses

A Thin Sheet of Plastic (N = 1 $\lambda$ = 700 Nm)losses