Jase Bentley

2022-12-31

A concave mirror has a focal length of 4 cm and an object 2 cm tall is placed 9 cm away from it. Find the nature and position of the image formed.

kunstgrenwa3

Beginner2023-01-01Added 7 answers

Focal length = f = - 4 cm

Height of object = + 2 cm

Object distance = u = - 9 cm

Image distance = v = ?

Height of image = size = h' = ?

From thew mirror formula

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

Putting all the values

$\frac{1}{v}-\frac{1}{9}=\frac{1}{-4}$

After solving

v=−7.2cm

As a result, the image is created 7.2 cm away from the mirror.

Now for finding magnification

We know,

$m=\frac{-v}{u}$

Putting all the values

$\frac{-(-7.2)}{-9}$

After solving

m=−0.8

As the magnification is negative, the image is real, inverted.

Height of object = + 2 cm

Object distance = u = - 9 cm

Image distance = v = ?

Height of image = size = h' = ?

From thew mirror formula

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

Putting all the values

$\frac{1}{v}-\frac{1}{9}=\frac{1}{-4}$

After solving

v=−7.2cm

As a result, the image is created 7.2 cm away from the mirror.

Now for finding magnification

We know,

$m=\frac{-v}{u}$

Putting all the values

$\frac{-(-7.2)}{-9}$

After solving

m=−0.8

As the magnification is negative, the image is real, inverted.

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