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Old Jun 25th 2009, 01:20 AM   #1
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Total internal reflection

Show that total internal reflection occurs for light entering normally one face of an isosceles right-angle prism of glass of n=1.5 but not in the case when light enters similarly a similar thin hollow prism filled with water of n=1.33.
n is the refractive index.

I can show that total internal reflection occurs for the glass prism. But from my calculations internal reflection would also occur in the water filled prism.
I first found the angle of refraction when the light entered the prism at 90deg. Then found the angle incident on the next surface and the critical angle. The angle of incidence is equal to the critical angle in both cases.
Where have i gone wrong?
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Old Jun 25th 2009, 03:09 AM   #2
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From the geometry of the problem, the ray is incident on the other surface at 45 deg.
The critical angle i.e. the min angle say @ at which TI Reflection occurs is given by

@ = Sin inverse ( R2 / R1) where R2 is the refractive index of the less optically dense medium, in this case air .

Calculations show that for water a @ = 48.7 deg is required whereas for glass, a @ = 41.8 deg only is required, which is satisfied here as the angle is 45 deg.
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Old Jun 26th 2009, 12:20 AM   #3
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sorry i don't understand. why is the ray incident on the other plane at 45deg? isn't the ray refracted when it enters the medium?
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