A light ray falling at an angle of `53^@` with the surface of a clean slab of ice of thickness `1.00m` is refracted into it at an angle of `37^@`. Calculate the time taken by the light rays to cross the slab. Speed of light in vaccum `=3xx10^8m//sec`.

Explanation

`mu`: refractive index of slab
By Snell's law
`mu_1sini=mu_2sinr`
`1xxsin53^@=musin37^@`
`4/5=muxx3/5impliesmu=4/3`
Speed of light in slab, `v=c/mu=(3xx10^8)/(4//3)=9/4xx10^8 m//sec`
In `Delta ABC`
`cos 37^@=(AB)/(AC)=(1)/(AC)`
`4/5=(1)/(AC)impliesAC=5/4m`
Time taken by light ray to cross the slab
`t=(AC)/(v)=(5//4)/(9//4xx10^8)=5/9xx10^-8sec`