Question

An object of 10cm high is kept at a distance of 45cm in front of a concave mirror of focal length 30cm. Find the position and size of the image. Also state the characteristics of the image.

Answer 1

Explanation:

By using mirror formula

Answer 2

Given:

An object of 10cm high is kept at a distance of 45cm in front of a concave mirror of focal length 30cm.

To find:

• Position and size of image
• Characteristic of image

Calculation:

Applying Mirror Formula:

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

$= > \: \dfrac{1}{( - 30)} = \dfrac{1}{v} + \dfrac{1}{( - 45)}$

$= > \: - \dfrac{1}{30} = \dfrac{1}{v} - \dfrac{1}{45}$

$= > \: \dfrac{1}{v} = \dfrac{1}{45} - \dfrac{1}{30}$

$= > \: \dfrac{1}{v} = \dfrac{ 2 - 3}{90}$

$= > \: \dfrac{1}{v} = \dfrac{ - 1}{90}$

$= > v = - 90 \: cm$

So image will be formed 90 cm in front of mirror.

$magnification = - \dfrac{v}{u}$

$= > magnification = - \dfrac{ (- 90)}{( - 45)} = - 2$

$= > magnification = - 2$

So, image will be real, inverted and enlarged.

$\therefore \: \dfrac{h}{o} = - 2$

$= > \: \dfrac{h}{10} = - 2$

$= > \: h = - 20 \: cm$

So, image height will be 20 cm.

Hope It Helps.