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What should be the value of angle theta ...

What should be the value of angle `theta` so that light entering normally through the surface AC of a prism `(n=3//2)` does not cross the second refracting surface AB?

Text Solution

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Light ray will pass the surface AC without bending since it is incident normally. Suppose it strikes the surface AB at an angle of incidence i.
`i=90-theta`
For the required condition:
`i gt C rArr 90^(@)-theta gt C`
or `sin (90^@-theta) gt sinC`
or `cos theta gt sinC= 1/(3//2)`
`=2/3` or `theta lt cos^(-1)(2/3)`
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