Question

$5$ cm high object is placed at a distance of $25$ cm from a converging lens of focal length $10$ cm. Determine the position, size and type of the image.

Answer 1

Given:
Height of object, $h_0=5cm$
Object distance, $u=-25cm$
Since the lens is converging, thus it is a convex lens.
Focal length of the lens, $f=10cm$
Using lens formula,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{1}{v}=\frac{1}{10}+\frac{1}{-25}=\frac{3}{50}$

$\Rightarrow v=\frac{50}{3}=16.7cm$

Thus, the image is formed $16.7cm$ right of the lens.

Now, we know
$\frac{u}{v}=\frac{h_i}{h_0}$

$\Rightarrow h_i=\frac{50}{3\times -25}\times 5=\frac{10}{3}=-.3.cm$

Thus, the size of the image is $3.3cm$. Negative sign shows that the image formed is real and inverted. Hence, the image formed is real and inverted and diminished.