Question

An object of 3 cm length is placed at 10 cm from the pole of a concave mirror of focal length 9 cm. What will be the size & position of the image?

I got answer v = -90 cm & h' = -27 cm

Answer 1

Given:

Object distance, u = 10 cm

Focal length, f = 9 cm

Size of object, O = 3 cm

To find:

Image distance, v=?

Size of image, I = ?

Formula used:

Lens equation is given by,

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

Magnification is given by,

Magnification=$\frac{Image size}{object size}$

Magnification=$\frac{Image distance}{object distance}$

Solution:

Lens equation is given by following formula,

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

Where f= focal length of the lens

u= object distance from the lens

v = image distance from the lens

According to Cartesian convention of lenses,

• The distance from the left of the lens is taken as negative. Thus, object distance is taken as negative and focal length is also taken negative.
• The distance from the right of the lens is taken as positive. Thus, image distance is taken as negative and focal length is also taken negative.

Now using lens equation,

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

$\frac{1}{-9} = \frac{1}{-10} + \frac{1}{v}$

$\frac{1}{v} =\frac{1}{-90}$

Thus, v = -90 cm

The negative image distance implies that the image formed is virtual image on the left side of the lens.

Magnification is given by,

Magnification=$\frac{Image distance}{object distance}$

M = $\frac{-90}{-10}$

M = 9

Magnification=$\frac{Image size}{object size}$

M = $\frac{I}{O}$

10 = $\frac{I}{3}$

I= 30 cm

Thus, size of image is 30 cm.

Answer 2

Given: Concave mirror

h' =3cm , u= -10cm , f= -9cm , v= ?

1/f = 1/v + 1/u

1/v +1/u = 1/f

1/v = 1/f - 1/u

1/v = 1/(-9) - 1/(-10)

1/v = - 1×10/9×10 + 1×9/10×9

1/v = -10+9/90

= -1/90

v = -90 cm

The image is formed at a distance of 90cm behind the mirror .

M = -v/u = height of image / height of object

M = -90/-10

M = 9cm

M = height of image / 3

9 = height of image / 3

height of image = 27 cm

Image is 27cm in height , virtual and erect .

{ and their is no minus in height of image means in 27 cm ans } Remember *

Hope its help you a lot

Thank you