Question

A convex lens forms an image of an object on a screen $30\text{cm}$ from the lens. When the lens is moved $90\text{cm}$ towards the object, the image is again formed on the screen. Then the focal length of the lens is

• A. $13\text{cm}$
• B. $24\text{cm}$
• C. $33\text{cm}$
• D. $40\text{cm}$

Answer 1

The correct option is B $24\text{cm}$

According to lens formula
$\frac{1}{30}-\frac{1}{-u}=\frac{1}{f}$
or $\frac{1}{30}+\frac{1}{u}=\frac{1}{f}\dots \dots \left(i\right)$
Similarly, $\frac{1}{120}+\frac{1}{u-90}=\frac{1}{f}\dots \dots \left(ii\right)$
Solving these two equations, we get
$f=24\text{cm}$

Why this question? Tip: If the image can be obtained on a screen- it is a real image. This implies that v is positive.