Question

The focal length of a biconvex lens is $f$. If we cut the lens into two equal pieces as shown in the figure, the focal length of each piece will be ___.

• A. $\frac{f}{2}$
• B. $2f$
• C. $f$
• D. $0$

Answer 1

The correct option is C $f$

According to lens maker formula,
$\frac{\text{1}}{\text{f}}$ =$\text{(n-1)(}$$\frac{\text{1}}{R_1}$-$\frac{\text{1}}{R_2}$$\text{)}$
where, $f$ is the focal length of the lens in the medium where it is kept and $n$ is the refractive index of the lens with respect to the medium. $R_1$ and $R_2$ is the radii of curvature of the lens of the two refracting surfaces.

After cutting the lens horizontally, radii of curvature do not change. That is, $R_1$ and $R_2$ will remain unchanged even if we cut the lens horizontally. Also the value of $n$ will remain unchanged. This means focal length, $\left(f\right)$ of the lens will remain unchanged even if it is cut horizontally.