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Chapter 13: Problem 253

Calculate the reflectance of a quarter-wave antireflection film, of magnesium fluoride \((\mathrm{n}=1.35)\) coated on an optical glass surface of index \(1.52\).

Short Answer

Expert verified
The reflectance of a quarter-wave antireflection film of magnesium fluoride coated on an optical glass surface with an index of 1.52 is approximately 0.35%.

Step by step solution

01

Identify relevant formulas and values

We will use the following reflectance formula for a quarter-wave antireflection film: \[R = \left(\frac{n_1-n_2}{n_1+n_2}\right)^2\] Where: - R is the reflectance - \(n_1\) is the refractive index of the antireflection film (magnesium fluoride) - \(n_2\) is the refractive index of optical glass surface From the exercise, we have the values for both \(n_1\) and \(n_2\): - \(n_1 = 1.35\) (magnesium fluoride) - \(n_2 = 1.52\) (optical glass surface)
02

Calculate the reflectance

Plug the values of \(n_1\) and \(n_2\) into the reflectance formula: \[R = \left(\frac{1.35-1.52}{1.35+1.52}\right)^2\] Now, perform the calculations inside the parentheses: \[R = \left(\frac{-0.17}{2.87}\right)^2\] Next, square the resulting fraction: \[R = 0.0035\] Finally, we can multiply the result by 100 to express the reflectance as a percentage: \[R \approx 0.35 \% \]
03

State the final answer

The reflectance of a quarter-wave antireflection film of magnesium fluoride coated on an optical glass surface with an index of 1.52 is approximately 0.35%.

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Most popular questions from this chapter

A metallic coating absorbs \(88 \%\) of the incident light. A thin film has one half the optical density of the coating. What is the transmittance of the film?

A collimated beam of light of wavelength \(\lambda\) falls at normal incidence ton a plate .of glass of index of refraction \(\mathrm{n}\) and thickness d. Give a formula for the fraction of the incident intensity that is transmitted. Find the numerical value of the transmittance for (a) \(\lambda_{\text {vac }}=5000.0000 \AA\) and (b) \(\lambda_{\mathrm{vac}}=5000.0416 \AA, \mathrm{n}=1.5, \mathrm{~d}=1 \mathrm{~cm}\)

What is the ratio of intensities of Rayleigh scattering for the two hydrogen lines \(\lambda_{1}=410 \mathrm{~nm}\) and \(\lambda_{2}=656 \mathrm{~nm}\) ?

Calculate the reflectance of a quarter-wave antireflection film, of magnesium fluoride \((\mathrm{n}=1.35)\) coated on an optical glass surface of index \(1.52\).

Visible light is incident on a medium whose coefficient of absorption is \(\alpha=0.10 \mathrm{~cm}^{-1}\). Find the ratios of the amplitude and intensity of the light after traveling distances of \(5 \mathrm{~cm}\), \(10 \mathrm{~cm}, 25 \mathrm{~cm}\), and \(50 \mathrm{~cm}\) in the medium compared to their values initially.
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