Question

What is the thinnest film of $Mg{F}_2\left(n=1.39\right)$on glass that

produces a strong reflection for orange light with a wavelength of 600 nm?

Short answer

The thinnest film should be of $216nm$thick that produces reflection of orange light.

Step-by-step solution

Given information

The reflected orange light has a wavelength of $\lambda =600nm=6\times {10}^{-7}m.$

The refractive index of the thin film is,$n=1.39$

Thickness of the film determination

The thickness of the thinnest film of $Mg{F}_2$can be obtained by the equation of constructive interference as, localid="1650048664982" $d=\frac{\lambda m}{2n}$, where $m=1,2,3......$

For thinnest film, consider $m=1$

Thus, thickness of the film should be,

localid="1650050646256" $$\begin{gathered} d=\frac{\lambda }{2n} \\ d=\frac{\left(6\times {10}^{-7}\right)m}{2\times 1.39} \\ d=2.16\times {10}^{-7}m \\ d=216nm \end{gathered}$$