Question

Four identical thin lenses are kept one beside the other on the same optical axis.The right surface of rightmost lens is silvered. Focal length of each lens is 20cm and radius of the silvered surface is 20cm.The focal length of the combined system is​

Answer 1

Answer:

The focal length of the combined system = f= - 2cm

Explanation:

Given :

Four identical thin lenses are kept one beside the other on the same optical axis

f1=f2=f3=f4=f=20cms

Radius of  curvature of mirror = 20cm

Focal length  of mirror= 20/2=10cms

Effective combined focal length of four lenses :

1/f eq= 1/f+1/f2+1/f3+1/f4= 4/f [ since f1=f1=f3=f4=f=20cm]

1/feq=4/20= 1/5

flens= 5cm

equivalent combination of lens - mirror combination :

1/f(mirror)-+2/f(lens) + = 1/f(eq)

=1/10 +2/5+=1/f eq

=4+1/10

=5/10

feq=10/5= 2cm

By sign conventions f=- 2cm