A glass cube is placed on a newspaper, which rests on a table. A person reads the news through the vertical side of the cube. Determine the maximum index of refraction of the cube.

Question

anonymous · Answer

What a beautiful Snell's Law question!  Assuming the reading angle is about half of 45 degrees, the maximum IOR for the glass to avoid total internal reflection seems to me to be about 2.6.

anonymous · Answer

On the other hand, assuming a reading angle of 45 degrees gets you a maximum IOR of 1.4.

rogue · Answer

Can you show me the work please? I don't understand how to get the ior for this :/

rogue · Answer

Ah, okay, awesome, I get now! =)

rogue · Answer

$$\sin \theta_c = \frac {n_2}{n_1}, n_2 = 1, \theta = \frac {pi}{2}, n_1 = \sqrt 2$$

rogue · Answer

Thank you so much =)

anonymous · Answer

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That's a drawing.  The angle of incidence of the light from the paper to the side of the cube is theta_1, and the angle of incidence of the light from the cube to your eye is theta_2.  theta_2 will be larger than theta_1 because of refraction, and the light bends away from the vertical when going into a medium of lower IOR, like air.  Snell's Law tells you the relationship between theta_1, theta_2, IOR_1 (glass) and IOR_2 (air, essentially 1).  The maximu for theta_2 is 90 degrees, because that will make the light simply reflect inside the cube and not get out to your eye at all.

One assumption you have to make is what is theta_1, the reading angle.  I initially picked 45/2, by drawing a picture of the cube, but maybe 45 is better.