An equilateral prism is kept in air and for a particular ray angle of minimum deviation is `38^@`. If the prism is immersed in water the angle of minimum deviation =........ Refractive index of water is 1.33

Explanation

`rArr (n_g)/(n_a) = (sin""((60 + 38)/(20))^(@))/(sin 30^@)`
Taking `n_a = 1 , n_g = (sin 49^@)/(sin 30^@) = 1.509`
When prism is immersed in water,
`n_(g)/(n_w) = (sin""((60 + delta_m)/(2)))/(sin 30^@)`
But `n_w = 1.33`
`therefore (1.509)/(1.33) =sin((60 + delta_m)/(2))^@/0.5`
`therefore sin ((60 + delta_m)/(2))^@ = (0.5 xx 1509)/(1.33) = 0.5673`
`therefore (60 + delta_m)/(2) = 34^@ 36.`
`therefore delta_m = 9^@ 12.`