Consider a coaxial system of two thin convex lenses of focal length f each separated by a distance d. Draw ray diagrams for image formation corresponding to an object at infinity placed on the principal axis in the following cases: (a) `d lt f`,(b)`d=f`, (c ) `f lt d lt 2f`, (d) `d=2f`, and (e) `d gt 2f`. Indicate the nature of the combination (concave, convex or plane) in each case.

Explanation

In each of two thin lenses separated by a distance d, we have
`(1)/(F) =(1)/(f_(1)) +(1)/(f_(2))-(d)/(f_(1)f_(2))`
For `f_(1)=f, f_(2)=f`,
`(1)/(F)=(1)/(f)+(1)/(f)-(d)/(f^(2))`
`F=(f^(2))/(2f-d)` (i)
So, if `d lt f` : F will be positive and `gt f`. So, the system will behave as a convex lens of focal length` lt f ` as shown in Figure.
b. If `d=f:F=f` i.e., the system will behave as a convex lens of focal length f as shown in Figure
c. If `f lt d lt 2f` : F will be positive and `lt f`, so the system will behave as a convex lens of focal length `gt f` as shown in Figure.
d. If `d=2f` : F will be indefinit, i.e., the system iwll behave as a plane glass plate of infinite focal length
If `d gt 2f` : F will become negative, i.e., the system will behave as concave lens as shown in Figure.