A ray of light is incident on a prism at an angle `50^(@)` and angle of prism is `60^(@)` and RI 1.5. Calculate the angle of total deviation (for non symmetric refraction).

Explanation

`A=60^(@), n=1.5, i_(1)=50^(@)`
Applying Snell.s law,
`n=(sin i_(1))/(sin r_(1))`
`sin r_(1)= (sin50^(@))/(1.5) = (0.7660)/(1.5) = 0.5106`
`r_(1)= sin^(-1) 0.5106`
`r_(1)=30^(@)42.`
But, `A=r_(1)+r_(2)`
`r_(2)=A-r_(1)=59^(@)60. - 30^(@)42.=29^(@)18.`
Also, `n=(sin i_(2))/(sin r_(2))`
`1.5=(sin i_(2))/(sin29^(@) 18.)`
`sin i_(2)= 1.5xx0.4894=0.7341`
`i_(2)=sin^(-1)(0.7341)=47^(@)14.`
`therefore d=i_(1)+i_(2)-A=50+47^(@)14. 60^(@)=37^(@)14.`