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A transparent cube of side d, made of a ...

A transparent cube of side d, made of a material of refractive index `mu_(2)` , is immersed in a liquid of refractive index `mu_(1)(mu_(1)ltmu_(2))`. . A ray is incident on the face AV at an angle `theta` (shown in the figure). Total internal refraction takes place at point E on the face BC. Then must satisfy:

A

` theta lt sin^(-1) sqrt(( mu_(2)^(2))/( mu_(1)^(2))-1)`

B

` theta gt sin^(-1) sqrt(( mu_(2)^(2))/( mu_(1)^(2))-1)`

C

` theta lt sin ^(-1) (mu_(1))/( mu_(2))`

D

` theta gt sin ^(-1) (mu_(1))/( mu_(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
` mu_(1) sin theta mu_(2) sin r_(1)`
`90 - r_(1) gt C `
`sin (90 - r_(1)) gt sin C `
cos `r_(1) gt sin c `
`cos r_(1) gt (mu_(1))/( mu_(2))`
`sqrt(1 - (( mu_(1) sin theta)/( mu_(2)))^(2)) gt (mu_(1))/(mu_(2))`
`1 - (mu_(1)^(2))/( mu_(2)^(2)) sin^(2) theta gt (mu_(1)^(2))/( mu_(2)^(2)) rArr (mu_(2)^(2) - mu_(1)^(2))/( mu_(1)^(2)) gt sin ^(2) theta `
`rArr theta lt sin ^(-1) sqrt(((mu_(2))/( mu_(1)))^(2)-1)`
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