It is given that the aispersive powers of crown and flint glasses are 0.06 and 0.10 respectively. Also the refractive indices for yellow light for these glasses are 1.517 and 1.621, respectively. We have to form an achromatic combination of prism of crown and flint glasses which can produce a deviation of `1^(@)` in the yellow ray. Evaluate the refracting angles of the two prisms needed.

Explanation

Crown glass, `omega=0.06,mu_(y)=1.517`
Flint glass, `omega'=0.10,mu_(y)'=1.621`
For no dispersion,
`(mu_(v)-mu_(r))A=(mu'_(v-mu'_(r))A'3`
`rArr omega(mu_(y)-1)A=omega'(mu'_(y)-1)A'`
`[omega=(mu_(v)-mu_(r))/(mu_(y)-1),omega'=(mu'_(v)-mu'_(r))/(mu'_(y)-1)]`
`rArr0.06(1.517-1)A=0.10(1.621-1)A'rArrA=2A'`
Deviation,
`delta_(0)=abs(mu_(y)-1)A-(mu_(y)-1)A')`
`1=abs((1.517-1)A-(1.621-1)A')`
`=abs((0.517-0.621A')`
`=abs(0.517xx2A'-0.621A')`
`rArr 1=0.413A'rArrA'=2.42^(@)`
`rArr`Angle of prism,A=2A'=`4.84^(@)`