For an achromatic combination, three different lenses are combined. Dispersive power of their material are `0.066,0.055 and 0.040` and their main focal length are - 22 cm, -11cm, and 'f' respectively then find the value of 'f' (in cm.)

Answer

`5 cm`

Explanation

`1/F=1/(f_(1))+1/(f_(2))+1/(f_(3)) Rightarrow (-df)/F^(2)= (-df)/(f_(1)^(2)) -(df_(2))/(f_(2)^(2))-(df_(3)^(2))/(f_(2)^(2))`
`omega/f=omega_(1)/f_(1)+omega_(2)/f_(2)+omega_(3)/f_(3)`
for achromastism `omega=0 Rightarrow (-0.066)/22-(0.055)/11+(0.040)/f=0`
`Rightarrow -3-5+40/f=0`
`f=5` cm