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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?

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Answer with Explanation:

We are given that

[tex]n_g=1.55[/tex]

[tex]n_f=1.35[/tex]

[tex]\lambda=521 nm=521\times 10^{-9} m[/tex]

[tex]1 nm=10^{-9} m[/tex]

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

Condition for destructive interference

[tex]2nt=(m+\frac{1}{2})\lambda[/tex]

[tex]t=\frac{(m+\frac{1}{2})\lambda}{2n}[/tex]

For minimum thickness m=0

Then, [tex]t=\frac{\lambda}{4n}[/tex]

b.Substitute the values

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

Cricetus

(a) The expression for minimum thickness is "[tex]2n_f t = (\frac{1}{2} )\lambda[/tex]".

(b) The minimum thickness is "97.8 nm"

Given:

  • ng = 1.55
  • nf = 1.35
  • λ = 521 nm

According to the question,

The optical path difference will be:

→ [tex]2n_ft[/tex]

The condition for destructive interference of reflected light will be:

→ [tex]2n_ft = (m+\frac{1}{2} )\lambda[/tex]

For minimum thickness,

  • m = 1

then,

→ [tex]2n_ft = (\frac{1}{2} )\lambda[/tex]

hence,

The minimum thickness will be:

→ [tex]t = \frac{\lambda}{4nf}[/tex]

By putting the values, we get

     [tex]= \frac{528}{4\times 1.35}[/tex]

     [tex]= \frac{528}{5.4}[/tex]

     [tex]= 97.8 \ nm[/tex]

Thus the responses above is right.

Learn more about reflection here:

https://brainly.com/question/14275936

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