Question

A thin convex lens of focal length $25cm$ is cut into two pieces $0.5cm$ above the principal axis. The top part is placed at $(0,0)$ and an object placed at $\text{(-50 cm, 0)}$. Find the coordinates of the image.

• A. $\text{(50 cm, -2 cm)}$
• B. $\text{(50 cm, -1 cm)}$
• C. $\text{(3 cm, -50 cm)}$
• D. $\text{(60 cm, -25 cm)}$

Answer 1

The correct option is B $\text{(50 cm, -1 cm)}$

Let AB be the principal axis of the convex len.

Focal length, $f=25cm$

since it cut into the piece $0.5cm$ above the principal axis.

The top part placed at $(0,0)$ and object is at $(50,0)$

So, Object distance, $u=50cm$

Let, the image distance be $v$.

Now, by using lens formula:

$\therefore \frac{1}{v}-\frac{1}{u}=\frac{1}{v}=\frac{1}{f}+\frac{1}{u}$

$\frac{1}{v}=\frac{1}{25}-\frac{1}{50}=\frac{1}{50}$

$v=50cm$

And, we know,

The magnification can be given as

$m=\frac{v}{u}=\frac{50}{-50}=-1$

Hence image is inverted.

so, $h^{\prime }=m\times h=-1\times 0.5=-0.5cm$

This would have formed $50cm$ from the pole and $0.5cm$ below the principal axis.

Hence, with respect to x-axis passing through the edge of the cut lens, the co-ordinates of the image are, $(50cm,(-0.5-0.5\left)cm\right)=(50cm,-1cm)$

$\therefore$ co-ordinates of the imag are $(50cm,-1cm)$