Combination Of Lenses (Compound Lenses)

In order to remove defects in the images formed by the lens, two or more lenses are combined together. Sometimes the combinations are  made by keeping the lenses in contact or they may be kept away from each other through some distance. Such combination of lenses is said to make a compound lens.

1. Two thin lenses in contact : When two thin lenses are placed in contact, the combination will act as a single lens called the equivalent lens.

                                    1/F = 1/f1 + 1/f2

 This formula is also true if one lens is convex and other is concave.

2. Two thin lenses separated by some distance : If two thin lenses are held a distance d apart from each other, then focal length of the combination is given by the relation,

                                   1/F = 1/f1 + 1/f2 – d/f1f2

Practice Problems :

1. Two converging lenses of equal focal length 'f' are placed in contact. Find the focal length of the combination.

Solution: F1  = F2  = f (given)

             Let focal length combination be F
By formula;
                   1/F = 1/F1 + 1/F2 
                         = 1/f   + 1/f
                         = (1+1)/f 
                         = 2/f
                      F = f/2

2. Two thin lenses (one convex and the other concave lens) of focal length 60 cm and 20 cm respectively placed in contact. Find the focal length of combination. 

Solution: F1 = 60 cm,  F2 = 20 cm,
              Focal length of combination (F) will be given by
            
                1/F = 1/F1 +1/F2
                1/F = 1/60 –1/20
                      = (1–3)/60
                      = –2/60
                 1/F = –1/30
                    F = –30 cm. (Ans.)