The dispersive power of crown and flint glasses are 0.02 and 0.04 respectively. If the difference between the refractive indices of blue and red colours is 0.012 for crown glass and 0.022 for flint glass, calculate the angle of the two prisms for a deviation of `8^(@)` (without dispersion).

Explanation

For crown glass,
`omega = 0.02` and `mu_(b) - mu_(r) = 0.012`
we know that,
`omega = (mu_(b) - mu_(r))/(mu - 1)`
`rArr (mu - 1) = (0.012)/(0.02) = 0.60`
For flint glass
`omega' = 0.04`
`mu'_(b) = mu'_(r) = 0.022`
`:. mu' - 1 = (0.022)/(0.04) = 0.55`
Again, `(delta)/(delta') = (omega)/(omega') = (0.04)/(0.02) = 2`
`rArr delta = 2 delta'`
Given that
`delta - delta' = 8^(@)`
`2delta' - delta' = 8`
`delta' = 8^(@)` and `delta = 16^(@)`
Now using the formula
`delta = (mu - 1) A`
A (for crown glass) ` (delta)/((mu - 1)) = (16)/(0.60) = 26.67^(@)`
A' (for flint glass) `= (delta')/((mu' - 1)) = (8)/(0.55) = 14.55^(@)`