Question

If an object 5cm high is placed at a distance of 12cm from a concave mirror of focal length 8cm, find the position, nature and height of the image formed.

Answer 1

Answer:

position of image is 4.8 cm away from the left side of mirror.

Nature of image will be real and inverted

height of image will be 2 cm.

Explanation:

distance of object from the mirror denoted by u = 12 cm

As we know focal length of concave mirror is always negative therefore

focal length of concave mirror (f) = -8 cm

height of object(h) = 5 cm

height of image (h') = ?

distance of image from the mirror (v) = ?

we can find image distance using mirror formula

1/f = 1/v + 1/u

1/(-8) = 1/v +  1/12

1/v =  - (1/8 + 1/12)

v = - 4.8 cm

Now as we know, magnification of  mirror is given by the ratio of height of image to height of object.

m =  h'/h

Also

m = -v/u

So,

h'/h = -v/u

h'/5 = -(-4.8)/(-12)

h' = -2 cm

So height of image will be 2 cm.

and here negative sign indicate that nature of image will be Real and inverted.

So position of image is 4.8 cm away from the left side of mirror.

Nature of image will be real and inverted

height of image will be 2 cm.