Question

an object is placed at a distance of 8cm from a convex mirror of focal lenght 12cm find the position of image.

Answer 1

hence the v value is 4.8cm so image formed is behind the mirror

Answer 2

Light

Convex mirror is type of spherical mirror in which bulging side faces the source of light. Convex mirror forms virtual, erect, and diminished image of the objects.

We've been given that an object is placed at a distance of 8cm from a convex mirror of focal lenght 12cm. With this information, we've been asked to find out the position of the image i.e. image distance.

Given:

Object distance, u = -8cm

Focal length, f = 12cm

To find:

Image distance, v = ?

We can find the image distance by using mirror formula.

A formula which gives the relationship between image distance, object distance and focal length of a sperical mirror is known as the mirror formula. Mathematically,

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

Where, v denotes distance of image, u denotes distance of object and f denotes focal length.

By using the mirror formula and substituting given values, we get:

$\implies \dfrac{1}{v} + \dfrac{1}{ - 8} = \dfrac{1}{12} \\ \\ \implies \dfrac{1}{v} - \dfrac{1}{8} = \dfrac{1}{12} \\ \\ \implies \dfrac{1}{v} = \dfrac{1}{12} + \dfrac{1}{8} \\ \\ \implies \dfrac{1}{v} = \dfrac{3 + 2}{24} \\ \\ \implies \dfrac{1}{v} = \dfrac{5}{24} \\ \\ \implies v = \cancel{\dfrac{24}{5}} \\ \\ \implies \boxed{v = 4.8}$

Hence, the image is formed at the distance of 4.8cm behind the mirror and is virtual and erect.