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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 angle of incidence `i`. The refrected and the refracted rays make an angle of `90^@` with each other. The angles of reflection and refraction are r and `r^'` respectively. The critical angle is
(i) `sin^-1(tanr)`
(ii) `sin^-1(tani)`
(iii) `sin^-1(tanr)`
(iv) `tan^-1(tani)`

A

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

B

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

C

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

D

`sin^(-1) (tanr')`

Text Solution

Verified by Experts

The correct Answer is:
A

From the figure , we find out `r + r' = 90^(@)` but `i= r " " therefore i+ r' = 90^(@) therefore r' = 90^(@) - i`
According to Snell's law,
`n_(d) sin i= n_(r) sin r' = n_(r) sin (90^(@) - i)`
`therefore (sin i)/(sin (90^(@) - i)) = (n_(r))/(n_(d))`
`therefore (sin i)/(cos i) = tani = (n_(r))/(n_(d)) " " ... (1)`
But sin C = `(n_(r))/(n_(d)) " " (2)`
`therefore` From (1) and (2) , tan i = sin C
`therefore C = sin^(-1) (tani) = sin^(-1) (tan r) (because i = r)`
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