**Anti-reflective coatings on lenses use thin-film interference to eliminate the reflection of a particular color. Suppose a glass lens (ng = 1.55) is covered with a thin film (nf = 1.35) to prevent green light (λ = 521 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:**

We are given that

n_g=1.55

n_f=1.35

\lambda=521 nm=521\times 10^{-9} m

1 nm=10^{-9} m

a.We have to find the expression for the minimum thickness the film can have ,t.

Condition for destructive interference

2nt=(m+\frac{1}{2})\lambda

t=\frac{(m+\frac{1}{2})\lambda}{2n}

For minimum thickness m=0

Then, t=\frac{\lambda}{4n}

b.Substitute the values

t=\frac{521\times 10^{-9}}{4\times 1.35}=96.5nm