Question

A concave mirror is used for image formation for different positions of an object. What inferences can be drawn about the following when an object is placed at a distance of $10cm$from the pole of a concave mirror of a focal length of$15cm$?

(a) Position of the image($v$)

(b) Size of the image($m$)

(c) Nature of the image

Draw a labeled ray diagram to justify your inferences.

Answer 1

Step 1: Given

Object distance ($u$) = $-10cm$ (object distance will be negative, as it is placed on the left side of the mirror)

Focal length($f$ )= $-15cm$ (focal length of the concave mirror is taken negatively)

Step 2: Calculate the magnification and distance of the image,

(a) Position of the image.-

Mirror formula $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

Substituting given values

$$\begin{gathered} \frac{1}{v}+\frac{1}{-10}=\frac{1}{-15} \\ \frac{1}{v}=\frac{3-2}{30} \\ \frac{1}{v}=\frac{1}{30} \\ v=+30cm \end{gathered}$$

The image will be formed $30cm$ behind the mirror as $v$ is positive.

(b) Size of image ($m$) -

The magnification formula $\frac{-v}{u}=\frac{-30}{-10}=3$

This means that the image is highly magnified.

(c) Nature of image - Since v is positive image will be virtual and erect

Step 3: DIAGRAM

The position of the image is $30cm$ behind the mirror. Its size is highly magnified, erect, and virtual in nature.