The index of refraction of heavy flint glass is `1.68` at `434 nm` and `1.65` at `671nm`. Calculate the difference in the angle of deviation of blue `(434 nm)` and red `(671 nm)` light incident at `65^@` on one side of a heavy flint glass prism with apex angle `60^@`.

Answer

B

Explanation

For blue light,
`mu=(sin i_1)/(sinr_1)`
or `1.68=(sin65^@)/(sinr_1)`
Solving this equation, we get
`r_1=32.6^@`
`r_2=A-r_1=27.4^@`
Again applying,
`mu=(sini_2)/(sinr_2 )or 1.68=(sin i_2)/(sin27.4^@)`
Solving this equation, we get
`i_2=50.6^@`
Now, `delta_B=i_1+i_2-A`
or `delta_B=65^@+50.6^@-60^@=55.6^@.....(i)`
For red light,
`1.65=(sin65^@)/(sinr_1)`
or `r_1=33.3^@`
`:. r_2=A-r_1=26.7^@`
Now, `1.65=(sini_2)/(sin26.7^@)`
`:. i_2=47.8^@`
`:. delta_R=i_1+i_2-A`
or `delta_R=65^@+47.8^@-60^@=52.8^@`....(ii)`
From Eqs (i) and (ii), we get
`delta_B-delta_R=2.8^@`