Max Angle and Destructive Interference

[nightseeress]

Homework Statement

Determine the maximum angle θ for which the light rays incident on the end of the the optical fiber of radius 1 mm are subject to the total internal reflection along the walls of the fiber. Assume that the fiber has an index of refraction of 1.3 and that the outside medium is air.

Homework Equations

sinθc = n2/n1

The Attempt at a Solution

sinθc = 1/1.3
θc = arcsin(1/1.3) = 50.28 degrees

However, the correct answer is 55 degrees. What am I doing wrong?

Homework Statement

A possible means for making an airplane invisible to radar is to coat the plane with an antireflective polymer coating. If the radar waves have frequency of 10GHz and the index of refraction of the polymer is n=1.5, how thick would you make the coating?

Homework Equations

2nt=mλ
c=fλ

The Attempt at a Solution

λ=c/f=(3x10^8)/(10x10^10)=0.003
2(1.5)t=(1)(0.003)= 1 mm

Correct answer is 5 mm. What am I doing wrong?

 

[anathema]

In both of your attempts, you have made a small mistake in your calculations. In the first problem, the index of refraction of the fiber should be n=1.3, not n=1. In the second problem, the frequency of the radar waves should be 10^10 Hz, not 10 GHz. These small mistakes can make a big difference in the final answer. Make sure to double check your values before plugging them into equations.

Also, in the first problem, the correct formula to use is sinθc = n2/n1, not sinθc = 1/n1. This will give you the correct answer of 55 degrees.

In the second problem, the correct formula to use is 2nt = (m+1/2)λ, not 2nt = mλ. This takes into account the extra half wavelength that is needed for the antireflective coating. Using this formula, you should get a thickness of 5 mm, which is the correct answer.

Hope this helps! Keep up the good work in your scientific studies.