As the ray of light grazes the second surface, `r_(2)` is the critical angle.
`sinr_(2)=(1)/(mu)`
`r_(2)=(45^@-r_(1))`
`sinr_(1)=(sin45^@)/(mu)=(1)/(sqrt(2)mu)`
`sinr_(2)=sin(45^@-r_(1))`
`=(1)/(sqrt(2))[cosr_(1)-sinr_(1)]`
`(1)/(mu)=(1)/(sqrt(2))[sqrt(1-(1)/(2mu^(2)))-(1)/(sqrt(2)mu)]`
`(1)/(mu)=(1)/(sqrt(2))[sqrt(2mu^(2)-1)/(sqrt(2)mu)-(1)/(sqrt(2)mu)]`
`2=sqrt(2mu^(2)-1)-1`
`2mu^(2)-1=9`
`2mu^(2)=10`
`rArr mu^(2)=5` or `mu=sqrt(5)`
At minimum deviation,
`r_(1)=r_(2)(45^(@))/(2)=22.5^(@)`
`mu=(sini_(1))/(sinr_(1))rArrsini_(1)=(sqrt(5))sin(22.5^(@))`
`i_(1)=58.8^(@)`