The refractive index of water and glycerine are 1.33 and 1.47 respectively. What is the critical angle for a light ray going from the latter to the former?

Options

A. `60^(@)`48'
B. `64^(@)`48'
C. `74^(@)`48'
D. None of these

Answer

B

Explanation

When a ray of light passes form glycerine ( denser `mu = 1.47`) to water (rate ` mu = 1.3` ) the angle of refraction (r) is greater than angle of incidence (i) , then from Snell's law
`(sin i)/(sin r) =(mu_(2))/(mu_(1)) lt 1`
When `r = 90^(@)`, corresponding of incidence is known as critical angle i.e., ` i = theta_(c)`
`therefore (sin theta_(c))/(sin 90^(@)) = (mu_(2))/(mu_(1))`
`rArr " "sin theta_(c) = (mu_(2))/(mu_(1))`
`rArr" "theta_(c) = sin^(-1)((mu_(2))/(mu_(1))) = sin^(-1)((1.33)/(1.47))`
`theta_(c) = 64^(@) 48'`