Fraction of light reflected inside a diamond

AI Thread Summary
The discussion centers on the application of Fresnel equations for light reflection in diamonds, specifically regarding total internal reflection at angles greater than the critical angle. The user initially calculated reflection coefficients for s and p-polarized light but encountered confusion regarding the transmitted angle, questioning the validity of Fresnel's equations beyond the critical angle. It was clarified that for angles exceeding the critical angle, the transmitted angle is not zero, and the reflection coefficient becomes complex with a magnitude of one. Despite this, the phase of the complex coefficient varies with the angle, and Fresnel's equations remain applicable. The conversation emphasizes the importance of understanding complex reflection coefficients in optical physics.
Davidllerenav
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Homework Statement
Diamonds have an index of refraction of n = 2.42 which allows total internal
reflection to occur at relatively shallow angles of incidence. What fraction of the light reflects for internal angles ##\theta_i = 40.5^°## and ##\theta_i = 50.6^°##?
Relevant Equations
Fresnel equations
Snell's law
So i do now that it is a case of total internal reflection, but i didn't get R=1 for ##\theta_i=40.5^°##. I used the Fresnel equations for both s and p-polarized light and for s I got ##r_s=\frac{n_i\cos\theta_i-n_t\cos\theta_t}{n_i\cos\theta_i+
n_t\cos\theta_t}=0.296## using ##n_i=2.42## and ##n_t=1##. For p I got ##r_p=\frac{n_i\cos\theta_t-n_t\cos\theta_i}{n_i\cos\theta_t+
n_t\cos\theta_i}=0.522##. What am I doing wrong?
 
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What values are you using for ##\theta_t##?
 
nasu said:
What values are you using for ##\theta_t##?
Well since both incident angles are greater than the critical angle ##\theta_c=24.4^°##, then ##\theta_t=0##.
 
Are Fresnel's equations still valid beyond the critical angle?
 
haruspex said:
Are Fresnel's equations still valid beyond the critical angle?
I thought so, but reading the chapter again I think not because the transmited angle isn't in facr zero, but complex.
 
Davidllerenav said:
Well since both incident angles are greater than the critical angle ##\theta_c=24.4^°##, then ##\theta_t=0##.
No, the angle is not zero. For angles larger than the critical angle there is no real ##\theta_c ##. The Fresnel reflection coefficient becomes a complex number with a magnitude of 1 for any angle larger than the critical angle. The phase of the complex coefficient still changes with the angle but the magnitude doesn't. Fresnel's equations are still valid. They can be written in terms of just incident angle and index of refraction so there is no problem with the transmission angle.
 
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