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^(@), sqrt(2)`
B. `40^(@), sqrt(2)`
C. `30^(@), (1)/(sqrt(2))`
D. `45^(@),(1)/(sqrt(2))`

Answer

A

Explanation

`A=60^(@), i=45^(@)` Angle of minimum deviation
`delta_("min")=i+e-A`,
(where e is the emergent angel by prism)
`=2i-A`
`=2xx45^(@)-60^(@)`
`delta_("min")=30^(@)`
Refractive index of the prism,
`mu=(sin((A+delta_("min"))/(2)))/(sin((A)/(2)))=(sin((60^(@)+30^(@))/(2)))/(sin30^(@))`
`=(sin45^(@))/(sin30^(@))=sqrt2`