A laser beam in vacuum enters a crown glass (n 1.5) D as shown, with flat side o

Question

A laser beam in vacuum enters a crown glass (n 1.5) D as shown, with flat side of the D vertical and on the right. The beam is at 50° to the horizontal when it hits the right side of the D at exactly the middle of the D. If you were to repeat this experiment (beam still at 50°), only now with the D complete submerged in a fluid of index n, what values of n would cause total internal reflection? (Note: there is a range of possible n, so your answer should not just be a single number.) Answer: n 2 2.0

Explanation / Answer

from snell's law  

ni sin(i) = nr sin(r)

when i = critical angle then r = 90 deg  

putting values,

n sin(50) = 1.5 sin(90)

n = 1.96

so any angle greater than this will go under ITR.

so n >= 1.96 OR n>= 2.0 (in two significant digits )

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