Question

an object 20 cm from a spherical mirror give rise to virtual image 15 cm from behind the mirror the type of the mirror and its focal length is...

Answer 1

Answer:

Ok

Explanation:

U =-20

V=15

1/v+1/u=1/f

1/15-1/20=1/f

4-3/60=1/f

1/60=1/f

F=60cm

Mirror=convex mirror

Answer 2

Given:

• Object distance = 20 cm.
• Image distance = 15 cm
• Image is virtual

To find:

• Type or mirror ?
• Focal length of mirror ?

Calculation:

First of all, let's calculate the magnification of the image :

$mag. = - \dfrac{v}{u}$

$\implies mag. = - \dfrac{15}{( - 20)}$

$\implies mag. = \dfrac{3}{4}$

$\implies mag. = 0.75$

• Since magnification value is positive but less than 1 , the image is erect and diminished.

So, mirror is convex.

• This is because convex mirror is able to produce a virtual, erect and diminished image.

Now, applying Mirror Formula:

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

$\implies \dfrac{1}{f} = \dfrac{1}{15} + \dfrac{1}{( - 20)}$

$\implies \dfrac{1}{f} = \dfrac{1}{15} - \dfrac{1}{20}$

$\implies \dfrac{1}{f} = \dfrac{4 - 3}{60}$

$\implies \dfrac{1}{f} = \dfrac{1}{60}$

$\implies f = 60 \: cm$

So, focal length of mirror is 60 cm.