A thin plane membrane separates hydrogen at `7^(@) C` from hydrogen at `47^(@) C`, both being at the same pressure. If a collimated sound beam travelling from the cooler gas makes an angle of incidence of `30^(@)` at the membrane, the angle of refraction is

Options

A. `sin^(-1) sqrt((7)/(32))`
B. `sin^(-1) sqrt((2)/(7))`
C. `sin^(-1) sqrt((4)/(7))`
D. `sin^(-1) sqrt((7)/(4))`

Answer

B

Explanation

`(sin i)/(sin r) = (v_(1))/(v_(2)) = sqrt((273 + 7)/(273 + 47)) = sqrt((280)/(320)) = sqrt((7)/(8))`
`(sin 30^(@))/(sin r) = sqrt((7)/(8))`
`r = sin^(-1) sqrt((8)/(28)) = sin^(-1) sqrt((2)/(7))`