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In the diagram shown a ray of light is i...

In the diagram shown a ray of light is incidetn on the interface between`1`&`2`at angle slightly greater than critical angle.The light suffers total internal reflections at this surface .After that the light ray falls at the interface at this interface .After that the light ray falls at the interface reflection..Which of the following relations should hold true?

A

`mu_(1)lt mu_(2)lt mu_(3)`

B

`mu_(1)^(2)-mu_(2)^(2)ltmu_(3)^(2)`

C

`mu_(1)^(2)-mu_(2)^(3)ltmu_(2)^(2)`

D

`mu_(1)^(2)+mu_(2)^(2)ltmu_(3)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B,C,D

For T.I.R at interface of`mu_(1)` &`mu_(2)`
`igtC rArr "Sin" i gt"Sin" C_(1)…….(1)`
taking refraction at interface of `mu_(1)` & `mu_(2)`
`mu_(1)"Sin"C_(1)=mu_(2)"Sin"90^(@) rArr "Sin"C_(1) =(mu_(1))/(mu_(2))…….(2)`
From (1)&(2)
`sin i gt (mu_(2))/(mu_(1))`
For I.T.R. at interface of `mu_(2)`&`mu_(3) 90^(@)-i gt C_(2)`
`sin(90^(@)-i)gt"Sin" C_(2) rArr cosigtsinC_(2).....(3)`
taking refractin at interface of `mu_(2)&mu_(3)`
`mu_(1)"Sin"C_(2)=mu_(3)"Sin"90^(@) rArr "Sin"C_(2) =(mu_(3))/(mu_(1)).............(4)`
from(3)&(4)
`"cos"igt(mu_(3))/(mu_(1)) rArr sqrt(1-sin^(2)i)gt(mu_(3))/(mu_(1))`
`1-(mu_(2)^(2))/(mu_(1)^(2))gt(mu_(3)^(2))/(mu_(2)^(1))`
`mu_(1)^(2)-mu_(2)^(2)gtmu_(2)^(3)`
`mu_(1)^(2)-mu_(3)^(2)gtmu_(2)^(2)`
obiously `mu_(1)^(2)-mu_(2)^(2)gtmu_(3)^(3)`
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