Chapter 24, Problem 76GP

(a)

To determine

Minimum thickness needed in order to eliminate blue reflections for light at normal incidence.

Answer to Problem 76GP

Minimum thickness is $t_{\min }=81.5\text{ nm}$

Explanation of Solution

Given:

Refractive index, $n=1.38$

Wavelength, $\lambda =450\text{ nm}$

Formula used:

Minimum thickness can be given as: $t_{\min }=\frac{\lambda }{4n}$

Calculation:

Substituting the given values,

  $\begin{array}{l}{t}_{\min }=\frac{\left(450\text{ nm}\right)}{4\left(1.38\right)}\\ t_{\min }=81.5\text{ nm}\end{array}$

Conclusion:

The minimum thickness is $t_{\min }=81.5\text{ nm}$

(b)

To determine

Minimum thickness needed in order to eliminate red reflections for light at normal incidence.

Answer to Problem 76GP

The minimum thickness is $t_{\min }=126.8\text{ nm}$

Explanation of Solution

Given:

Refractive index, $n=1.38$

Wavelength, $\lambda =700\text{ nm}$

Formula used:

Minimum thickness can be given as: $t_{\min }=\frac{\lambda }{4n}$

Calculation:

Substituting the given values,

  $\begin{array}{l}{t}_{\min }=\frac{\left(700\text{ nm}\right)}{4\left(1.38\right)}\\ t_{\min }=126.8\text{ nm}\end{array}$

Conclusion:

The minimum thickness is $t_{\min }=126.8\text{ nm}$