Light travels in two media A and B with speeds `1.8 × 10^(8) m s^(–1) and2.4 × 10^(8) m s^(–1)` respectively. Then the critical angle between them is

Options

A. ` sin^(-1)(2/3)`
B. `tan^(-1)(3/4)`
C. `tan^(-1)(2/3)`
D. `sin^(-1)(3/4)`

Answer

D

Explanation

Here, `v_(A) = 1.8 xx 10^(8) ms^(-1), v_(B) = 2.4 xx 10^(8) ms^(-1)` Light travel slower in denser medium. Hence medium A is a denser medium and medium B is a rarer meedium. Here , light travels from medium A to medium B. Let the the critical angle between them.
`:. sin C = .^(A)mu_(B) = (1)/(.^(B)mu_(A)) = (1)/(.^(B)mu_(A)) = (v_( A))/(v_(B)) ( :'.^(1)mu_(2) = (v_(1))/(v_(2)))`
` :. sin C = (v_(A))/(v_(B)) = (1.8 xx 10^(8))/(2.4 xx 10^(8)) = 3/4` or `C = sin^(-1)(3/4)`