Question

An object is placed at a distance of 30 cm from a concave lens of a focal length of 15 cm. List four characteristics (Nature, Position, etc.) of the image formed by the lens.

Answer 1

Given:

The object distance, $u=-30$

The focal length of the mirror, $f=15cm$

Finding the image distance using the mirror formula:

We know that $\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$

$$\begin{gathered} Bysubstitutingthegivenvalues,weget \\ \frac{1}{-30}+\frac{1}{v}=\frac{1}{15} \\ \Rightarrow \frac{1}{v}=\frac{1}{15}+\frac{1}{30} \\ =\frac{3}{30} \\ =\frac{1}{10} \\ Therefore,v=10cm \\ Magnificationisgivenby, \\ \frac{v}{u}=\frac{1}{3} \end{gathered}$$

Therefore, the nature of the image formed by the lens is:

1. Erect,
2. Virtual,
3. 1/3 size of the object,
4. 10 cm between lens and object.