Question

The biconvex lens has a focal length $f$. It is cut perpendicular to the principal axis passing through the optical center, then the focal length of each half is

• A. $f$
• B. $f/2$
• C. $3f/2$
• D. $2f$

Answer 1

The correct option is B

$f/2$

Step 1: Given Data

A biconvex lens of focal length $f$,

It is cut perpendicular to the axis and through the optical center.

Step 2: Formula Used

The lens maker's formula is $\frac{1}{f}=(n-1)(\frac{1}{R_1}-\frac{1}{R_2})$

Where $f$ is the focal length of the lens

$n$ is the refractive index of the material

$R_1$ is the radius of the first part

$R_2$ is the radius of the second part

Step 3: Calculating the focal length of the biconvex lens

The diagrammatic representation of the given case is,

Let the focal length before cutting be $f$

⇒ $\frac{1}{f}=(n-1)(\frac{1}{R}-\frac{1}{-R})$

⇒ $\frac{1}{f}=(n-1)(\frac{1}{R}+\frac{1}{R})$

⇒$\frac{1}{f}=(n-1)\left(\frac{2}{R}\right)$

Step 4: Calculating the focal length of the lens after it's been cut

Let the focal length of the lens after it's been cut is $f\text{'}$

For the plano-convex lens,

⇒$\frac{1}{f\text{'}}=(n-1)(\frac{1}{R}-\frac{1}{\infty })$

⇒$\frac{1}{f\text{'}}=(n-1)\left(\frac{1}{R}\right)$

⇒$\frac{1}{f\text{'}}=\frac{2}{f}$

⇒ Thus, the focal length after it's been cut is $f\text{'}=f/2$.

Hnece, option B is the correct answer.