a. Determine the 'effective focl length ' of the combination of the two lenses in Exercise 9.10, if they are placed 8.0 cm apart with their principal axes coincident . Does the answer depend on which side of the combination a beam of parallel light is incident? in the notion of effective focal length of this system useful at all ?

Explanation

a. `(1)/(v_(1)) - (1)/(u_(1)) = (1)/(f_(1))`
We have - `(1)/(- infty) + (1)/(v_(1)) = (1)/(30) " " therefore v_(i) = 30 ` cm
The image so formed acts as an object placed at 30- 8 = 22 cm from the convex lens on the right hand side.
`therefore (1)/(v_(2)) - (1)/(u) = (1)/(f_(2)) , (1)/(v_(2)) - (1)/(22) = (1)/(-20)`
Solving `rArr v_(2) = - 220 `cm
ther parallel of beam of light appears to diverge from 220 - 8 = 212 cm from the convex lens from left. Now when parallel beam of light is incident on the convec lens after which convex lens is plaed at 8 cm , `(1)/(v_(1)) - (1)/(u_(1)) = (1)/(f_(1)) , (1)/(v_(1)) - (1)/(- infty)= (1)/(-20) " " therefore v_(1) = - 20` cm
The image is formed -20 cm the left of concave lens and `therefore` it is 20 + 8 = 28 cm to the left of convex lens. ` (1)/(v_(2)) - (1)/(u_(2)) = (1)/(f_(2)) , (1)/(v_(2)) - (1)/((-28)) = (1)/(30)` , solving `v_(2) = -420 ` cm i.e., the light apprears to diverage from a point at 420 cm to the left of convex lens .
this shows that the answer depends on the side of incidence. so the notion of the effective focal length is not useful in this case.