The refracting angle of a glass prism is `60^(@)` and the refractive index of glass is 1.6. If the angle of incidence of a ray of light on the first refracting surface is `45^(@)` Calculate the angle of deviation of the ray . Given that `sin 26^(@)14' = 0.4419, " " sin33^(@)46' = 0.5558 and sin62^(@)47' = 0.8893`

Explanation

`"Hence" " " A = 60^(@) , mu = 1.6`
Angle of incidence on the first face ` = i_(1) = 45^(@)`
For refraction on the first face, `mu = (sini_(1))/(sinr_(1))`
`therefore " " sinr_(1) = (sini_(1))/(mu) = (sin45^(@))/(1.6)`
`= (1)/(sqrt(2) xx 1.6) = 0.4419 = sin26^(@).23^(@)`
`or, " " r_(1) = 26^(@)23^(@)`
`"We know", " " A = r_(1) + r_(2)`
`therefore " " r_(2) = A - r_(1) = 60^(@) - 26.23^(@) = 33.77^(@)`
For refraction at the second face,
`mu = (sini_(2))/(sinr_(2)) or, 1.6 = (sini_(2))/(sin33.77^(@))`
`or, " " i_(2) = 62.9^(@)`
So, the angle of deviation,
`delta = i_(1) + i_(2) - A = 45^(@) + 62.8^(@) - 60^(@) = 47.8^(@)`