The refractive index of the crown glass for violet and red lights are 1.51 and 1.49 respectively and those of flint glass are 1.77 and 1.73 respectively. A narrow beam of white light is incident at a small angle of incident on shown combination of thin prism. Find values of `alpha` for which mean deviation of beam is zero. Also calculate net dispersing.

Explanation

Here, for crown glass, prism,
`mu_(b) = 1.51, mu_(r) = 1.49, A = 6^(@)`
and for flint glass prism,
`mu'_(b) = 1.77 and mu'_(r ) = 1.73, A' = ?`
Now, `mu = (mu_(b) + mu_(r ))/(2) = (1.51 + 1.49)/(2) = 1.50`, and `mu' = (mu'_(b) + mu'_(r ))/(2) = (1.77 + 1.73)/(2) = 1.75`
For no deviation, the conditions is
`delta + delta' = 0`
`(mu - 1) A + (mu' - 1) A' = 0`
`:. A' = (-(mu - 1)A)/((mu' - 1)) = (-(1.50 - 1)6^(@))/((1.75 - 1))`
`= (-0.50 xx 6^(@))/(0.75) = -4^(@)`
Negative sign implies that the two prisms must be combined in opposition.
Net dispersion `= (mu_(b) - mu_(r ))A + (mu'_(b) - mu'_(r))A'`
`= (1.51 - 1.49) 6^(@) + (1.77 - 1.73)(- 4)`
`= 0.02 xx 6 + 0.04 (- 4)`
`= 0.12 - 0.16 = - 0.04^(@)`