A ray of light suffers minimum deviation through a prism of refractive index `sqrt(2)`. What is the angle of prism if the angle of incidence is double the angle of refraction within the prism?

Explanation

In the case of minimum deviation,
`i_(1)=i_(2), r_(1)=r_(2)`
`delta=2i-A`
`r=A//2`
According to problem , `i=2r=A`
`delta_(min)=2A-A=A`
`n=(sin((A+delta_(min))/(2)))/(sin((A)/(2)))=(sinA)/("sin"(A)/(2))=(2"sin"(A)/(2)"cos"(A)/(2))/("sin"(A)/(2))`
`"cos"(A)/(2)=(n)/(2)=sqrt(2)/(2)=(1)/(sqrt(2))`
`A=90^@`