Question

an object of 2cm hight is placed at a distance of 20cm from the concave mirror of 10cm focal length .Find the position an size of the mirror​

Answer 1

Explanation:

The mirror is concave, f=-10cm,u=-15cm, 1/v= (u-f)/uf= [-15-(-10)]/150=-1/30, so, v=-30cm. So, the image is formed in the same side of the object at a distance of 30cm

Answer 2

Given :

• An object of 2 cm height is placed at a distance of 20 cm from the concave mirror of 10 cm focal length .

⇒ Object height , ho = 2 cm

⇒ Object distance , u = 20 cm

⇒ Focal length , f = 10 cm

To Find :

• position and size of the image of the mirror

Solution :

Use mirror formula .

$\implies \bf \dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}\\\\\implies \bf \dfrac{1}{10}=\dfrac{1}{20}+\dfrac{1}{v}\\\\\implies \bf \dfrac{1}{v}=\dfrac{1}{10}-\dfrac{1}{20}\\\\\implies \bf \dfrac{1}{v}=\dfrac{10}{200}\\\\\implies \bf v=20\ cm$

So , Image distance , v = 20 cm

We know that , Magnification ,

$\implies \bf m=\dfrac{-v}{u}\\\\\implies \bf m=\dfrac{(-20)}{20}\\\\\implies m=-1$

Since , magnification , m is -ve . So the image formed is real and inverted .

Now ,

$\implies \bf m=\dfrac{h_i}{h_o}\\\\\implies \bf 1=\dfrac{h_i}{2}\\\\\implies \bf h_i=2\ cm$

So , height of the image is 2 cm.