The angle of minimum deviation for a glass prism with `mu=sqrt3` equals the refracting angle of the prism. What is the angle of the prism?

Explanation

The releationship between refractive index, prism angle A and angle of minimum deviation is give be
`" " mu=sin[((A+D_(m)))/(2)]/(sin((A)/(2)))`
Here
`:.` Given `" " D_(m)=A`
Substituting the value, we have
`:. " " mu=(sinA)/(sin.(A)/(2))`
On solving, we have `" " =(2sin.(A)/(2)cos.(A)/(2))/(sin.(A)/(2))=2cos.(A)/(2)`
`:. " "mu=(sinA)/(sin.(A)/(2))=(2sin.(A)/(2)cos.(A)/(2))/(sin.(A)/(2))=2cos.(A)/(2)`
For the given value of refractive index,
we have
`:. " " cos.(A)/(2)=(sqrt3)/(2)`
or `" " (A)/(2)=30^(@)`
`:. " " A=60^(@)`
This is the required value of prism angle.