1.

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 angles of the two prisms for a deviation of 2^(@) without dispersion.

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Solution :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.


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