Question

A concave mirror produces three times enlarged image of an object placed at 10cm in front of it. Calculate the focal length of the mirror. Show the image formation with the help of react is placed 6cm away from the pole of a convex mirror

Answer 1

Answer:

15 cm

Explanation:

The mirror produces three times enlarged image.

So, magnification(m) = 3

WE KNOW, magnification of spherical mirrors = m = -v/u

Where v is the distance between image and mirror and u is the distance between object and mirror.

Here, u = -10 cm

=> 3 = -V/-10

=>v = 30

So , the distance between image and mirror = 30 cm

1/v + 1/u = 1/f(mirror formula)

1/30 + 1/-10 = 1/f

1/30 - 1/10 = 1/f

-2/30 = 1/f

-1/15 = 1/f

f = 15 cm

We know radius of curvature = 2f

So, radius of curvature = R = 2*-15 = -30 cm which is the required answer.

SHORTCUT -

Remember the formula, m = f/(f-u)

So, 3 = f/(f-(-10))

3 = f/(f+10)

Cross multiply,

3f + 30 = f

2f = -30

R = -30 cm (R= 2f).

Answer 2

Explanation:

Given,

Magnification, m=3

Object distance, u=10cm

We know,

Magnification, m=−uv

3=−10−v

⇒  v=30cm

From mirror formula,

f1=v1+u1

f1=301−101

=30×1010−30

=300−20

f=−15cm

Focal length, f=−15cm

I hope this answer will help you dear....