Question

12.
An object is placed at a distance of 10 cm
from a convex mirror of focal length
15 cm. Find the position and nature of
the image.​

Answer 1

Answer:

u=-10cm

f=15cm

Now, from the equation 1/f=1/v+1/u

1/15=1/v-1/10

5/30=1/v

Hence, v=6cm

Answer 2

Given,

An object is placed at a distance of 10 cm  from a convex mirror of focal length 15 cm.

To Find,

The position and nature of the image.

Solution,

The distance between the object and the mirror (u) = -10 cm

Focal length (f) = 15 cm

Position of the image formed (v) = ?

According the the mirror formula →

$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$

As we have to find v, we can write the formula as:

$\dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u}$

Substituting the values:

$\dfrac{1}{v}=\dfrac{1}{15}+\dfrac{1}{10}$

By making the denominators same through LCM,

→ LCM of 15 and 10 is 30

Therefore,

$\dfrac{1}{v}=\dfrac{2+3}{30}=\dfrac{5}{30}$

As $\dfrac{1}{v}=\dfrac{5}{30}$,

v = 6 cm

So, the image is located 6 cm behind the mirror.

Nature of the image formed:

As the mirror is a convex one, the image formed would be virtual and erect and would be located behind the mirror.

Knowledge Bytes:

A convex mirror is a spherical mirror with the reflecting surface bulging out. It reflects light outwards without bringing the light on focus.