Question

The given lens is broken into four parts rearranged as shown. If the initial focal length is $f$, then after rearrangement the equivalent focal length is

• A. $f$
• B. $\frac{f}{2}$
• C. $\frac{f}{4}$
• D. $4f$

Answer 1

The correct option is B $\frac{f}{2}$

When a lens is spliced longitudinally (along the principal axis), the resulting two half-lenses have the same focal length as the original full lens.


i.e $f_{(1+2)}=f_{(3+4)}=f$

If the two halves are spliced transversely (perpendicular to principal axis), the focal length of each of their halves is doubled.


$f_1=f_2=f_3=f_4=2f$

Now, if 1, 2, 3 and 4 are stacked one after the other, net focal length is given by

$\frac{1}{f_{net}}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}+\frac{1}{f_4}$
$=\frac{4}{2f}$
$\Rightarrow f_{net}=\frac{f}{2}$