Question

a converging mirror forms as real image of height 4 cm and object height 1 cm placed 20 CM away from the mirror
calculate the image distance.
what is the focal length
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Answer 1

ans

Converging mirror is actually concave mirror!

hi = 4cm

ho = 1cm

u=-20cm

(a) v=?

hi/ho=-v/u

where,

hi=height of the image

ho=height of the object

v=distance of the image from the mirror

u=distance of the object from the mirror

4/1=-v/-20

4 = v/20

v = 80cm

Let focal length of the mirror to be 'f'

1/f = 1/v + 1/u

1/f = 1/80 + 1/(-20)

1/f = 1/80 - 1/ 20

1/f = -3/80

f = -80/3 cm

Answer 2

# Converging mirror is actually concave mirror!

hi = 4cm

ho = 1cm

u=-20cm

(a) v=?

hi/ho=-v/u

where,

hi=height of the image

ho=height of the object

v=distance of the image from the mirror

u=distance of the object from the mirror

4/1=-v/-20

4 = v/20

v = 80cm

Let focal length of the mirror to be 'f'

1/f = 1/v + 1/u

1/f = 1/80 + 1/(-20)

1/f = 1/80 - 1/ 20

1/f = -3/80

f = -80/3 cm

                                                OR

Given :-

Image height (hi) = - 4cm

Object height (ho) = + 1cm

Object distance (u) = - 20cm

To find :-

Image distance (v)

Focal length (f)

Solution :-

According to the Mirror Magnification

→ m = -v/u = hi/ho

→ -v/u = hi/ho

→ -v/(-20) = -4/1

→ v/20 = -4

→ v = - 80cm

Now, according to Mirror Formula

→ 1/v + 1/u = 1/f

→ -1/80 + (-1)/20 = 1/f

→ -1/80 - 1/20 = 1/f

→ -1 - 4/80 = 1/f

→ 1/f = -5/80

→ 1/f = -1/16

→ f = -16cm

Hence,

Image distance = -80cm

Focal length = - 16cm

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