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A ray of light from a denser medium stri...

A ray of light from a denser medium strikes a rarer medium at an angle of incidence I (see figure ). The reflected and refracted rays make an angle of `90^(@)` with each other. The angles of reflection and refraction are r and `r^(')` . The critical angle is

A

`sin ^(-1)` (tan r)

B

`sin ^(-1)` (cot i)

C

`tan^(-1)` (Sin r)

D

`tan^(-1)` (sin i)

Text Solution

Verified by Experts

The correct Answer is:
A
Applying SneH.s Law for refraction`sini/sinr = n_(2)/n_(1)` ….(i)
From the given condition, r + `r^(.)` = 9
implies sin `r^(.)` = cos r ….....(2)
Solution of (1) and. (2) yields`sini/cosr=n_(2)/n_(r)` …...(3)
According to the Law for refraction,
i = r .....(4)
Using (3) and (4) we obtain
`sini/cosi=n_(2)/n_(1)` .....(5)
Also sin`theta_(c)=n_(2)/n_(1)`,Using(5)We obtain`theta_(c)=sin_(-1)`(tani)=`sin_(-1)`(tanr)
Hence (A) is correct.
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