Question

An object is placed at a distance of 10cm from a convex mirror of focal length 5cm
1. Draw a ray diagram showing the formation of the image
2. State two characteristics of the image formed
3. Calculate the distance of the image from mirror

Answer 1

as we have to find the distance of the image formed with the convex mirror so we can find it out by using the mirror formula which is
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
In case of the convex mirror focus is located at the right side of the mirror and the object is located at the left but image is always formed at the right side of the mirror.

Complete step by step answer
(1).

(2).
The characteristic of the image are:
As from the figure we can see that the image formed
(a) The image is virtual and erect (because the image formed is on the same side i.e. upper part from the principal axis.
(b) The image is not magnified because the size of image formed is smaller than the size of object
(3). As we have to find the distance of image formed which can be simply find out using the mirror formula i.e.
=> $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
=> $\dfrac{1}{5}$ = $\dfrac{1}{v}$ + $\left( {\dfrac{1}{{ - 10}}} \right)$;
Here focus of the mirror is positive and object distance $\left( u \right)$is negative because object is at left side of the mirror
=> $\dfrac{1}{v}$ = $\left( {\dfrac{{2 + 1}}{{10}}} \right)$
=> $\dfrac{1}{v}$ = $\left( {\dfrac{3}{{10}}} \right)$
=> $v$ = 3.33cm

Note: As we can see that value of $v$ = 3.33cm is positive so it is clear that the image formed at the right side of the mirror.
Value of focal length in convex is positive and the focal length of concave mirror is negative.
But in case of Lens focal length of convex lens is negative and focal length of concave is positive.
Convex mirrors always form virtual and erect images.