The angle of incidence for a ray of light at a refracting surface of a prism is `45^@`. The angle of prism is `60^@`. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are

Options

A. `30^@,sqrt2`
B. `45^@,sqrt2`
C. `30^@,(1)/(sqrt2)`
D. `45^@,(1)/(sqrt2)`

Answer

A, B, C

Explanation

i+e=A+`delta`
`45^@+45^@=60^@+delta_m [because i=eimplies delta=delta_m]`
`therefore delta_m=30^@`

`mu=(sin((delta_m+A)/(2)))/(sin""A/2)`
`=(sin((60^@+30^@)/(2)))/(sin((60^@)/(2)))`
`=(sin45^@)/(sin 30^@)`
`=(1)/(sqrt2)xx2/1`
`=sqrt2`