Question

lens is cut along the principal axis then there will be no change in the focal length of lens. but it is cut perpendicular to principal axis, then focal length will be twice the original one.why???

Answer 1

Answer:

Explanation:

The focal distance f of a lens can be calculated using a lensmaker's equation:

1/f = (n - 1)(1/R_1-1/R_2),

where n is a refractive index, R_1 and R_2 are curvature radii. For a biconvex lens the R_2 is taken negative. If |R_1| = |R_2| = R, we have

f = R/(2*(n-1)).

If one cuts lens perpendicularly to the principal axis, the obtained lens will be convex only on the one side and flat on another side: R_1 = R and R_2 = infinity. So,  

1/f_1= (n-1)/R   =>f_1=R/(n-1)=2f.