The dispersive power of the material of a lens is `0.04` and the focal length of the lens is `10cm`. Find the difference in the focal length (in mm) of the lens for violet and red colour.

Answer

4

Explanation

`1/f=(n-1)(1/(R_(1))-1/(R_(2)))implies-(df)/(f^(2))implies-(df)/(f^(2))=(1/(R_(1))-1/(R_(2)))dn`
(differentiating both sides)
`implies-(df)/f(n-1)(1/(R_(1))-1/(R_(2)))=(1/(R_(1))-1/(R_(2)))dn`
`=-df=f(dn)/(n-1)`
but `dn-v_(v)-n_(R):.-df=(n_(v)-n_(R))/(n-1)f`
`impliesdf=-wfimpliesf_(v)-f_(R)=-wf`
`=-0.04xx10=0.4cm`
`f_(R)-f_(v)=4mm`