Material `A` has critical angle `i_(A)`, and material `B` has critical angle `i_(B)(i_(B)gti_(A))`. Then which of the following is true
(i) Light can be totally internally reflected when it passes from `B` to `A`
(ii) Light can be totally internally relected when it passes from `A` to `B`
(iii) Critical angle for total internal reflection is `i_(B)-i_(A)`
(iv) Critical angle between `A` and `B` is `sin^(-1)((sini_(A))/(sin i_(B)))`

Options

A. `(i)` and `(iii)`
B. `(i)` and `(iv)`
C. `(ii)` and `(iii)`
D. `(ii)` and `(iv)`

Answer

D

Explanation

We know `C=sin^(-1)((1)/(mu))`
Given critical angle `i_(B)gti_(A)`
So `mu_(B) lt mu_(A)` i.e. `B` is rarer and `A` is denser.
Hence light can be totally internally reflected when it passes `A` to `B`
Now cirtical angle for `A` to `B`
`C_(AB)=sin^(-1)((1)/(._(B)mu_(A)))=sin^(-1)[._(A)mu_(B)]`
`=sin^(-1)[(mu_(B))/(mu_(A))]=sin^(-1)[(sin i_(A))/(sin i_(B))]`