The dispersive powers of crown and flint glasses are `0.03 and 0.05` respectively. The difference in refractive indices for blue and red colour is `0.015` for crown glass and `0.022` for flint glass. Calculate the angles of the two prisms for a deviation of `2^@` without dispersion.

Answer

`A = 10^(@)` ; `A = 6.82^(@)`

Explanation

Here, for crown glass :
`mu_(b) - mu_( r) = 0.015`
`omega = 0.03`
for flint glass :
`mu'_(b) - mu'_(r ) = 0.022`
`omega' = 0.05`
Net deviation `= (mu - 1)A + (mu' - 1)A' = 2^(@)`
`= (A(mu_(b) - mu_(r ))(mu - 1))/((mu_(b) - mu_( r))) + (A'(mu' - 1)(mu'_(b) - mu'_(r )))/((mu'_(b) - mu'_( r)))`
`= (A(mu_(b) - mu_(r )))/(omega) + (A'(mu'_(b) - mu'_(r )))/(omega')`
`= (A xx 0.015)/(0.03) + (A' xx 0.022)/(0.05)`
`2^(@) = (1)/(2) A + (11)/(25)A'`
For no dispersion,
`(mu_(b) - mu_(r ))_(A) + (mu'_(b) - mu'_(r ))A' = 0`
`A(0.015) + A'(0.022) = 0`
`A = -(22)/(15)A'`
Put in (i)
`(1)/(2)(-(22)/(15)A') + (11)/(25)A' = 2`
`- (44)/(150)A' = 2, A' = (-300)/(44) = - 6.82^(@)`
From (ii), `A = -(22)/(15) xx ((-300)/(44)) = 10^(@)`
Negative sign of `A'` implies that two prisms must be placed in opposition.