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)=1.8xx10^(8) m s^(-1), v_(B)=2.4xx10^(8) m s^(-1)`
Light travels slower in denser medium. Hence, medium A is a denser medium and medium B is a rarer medium.
Here, light travels from medium A to medium B.Let C be the critical angle between them.
`:.sinC-.^(A)mu_(B)-(1)/(.^(B)mu_(A))`
Refractive index of medium B w.r.t. to medium A is
`.^(A)mu_(B)=("Velocity of light in medium" A)/("Velocity of light in medium" B)=(v_(A))/(v_(B))`
`:.sinC=(v_(A))/(v_(B))=(1.8xx10^(8))/(2.4xx10^(8))impliesC=sin^(-1)((3)/(4))`