Question

Anti-reflective coatings on lenses use thin-film interference to eliminate the reflection of a particular color. Suppose a glass lens (ng = 1.56) is covered with a thin film (nf = 1.39) to prevent green light (λ = 536 nm) from being reflected.

(a) Write an expression for the minimum thickness the film can have, t.
(b) Calculate the minimum thickness, t, in nanometers?

Answer 1

λ = 536 nm

a) Wave 1 and 2 get superpose without reflection.

1 and 2 performs destructive interference.

$(2n_ft + \frac{λ}{2}) – \frac{λ}{2}$ = ∆ = path difference

For destructive interference

$∆ = (2N + 1)\frac{λ}{2} \\ 2n_ft = (2N + 1)\frac{λ}{2} \\$

For minimum thickness N = 0

$t = \frac{λ}{4n_f}$

b) $t_{min} = \frac{536}{4 \times 1.39} = 96.4023 \; nm$