Question

A converging mirror forms a real image of height 4 cm of an object of height 1 cm placed 20 cm away from the mirror
calculate the image distance. What is the focal length of the mirror?​

Answer 1

Answer:

the focal length is -80/3

Explanation:

      given

       height of the object = 1

       height of the image = -4 as it is a real and inverted image

       object distance = -20

   magnification =  -  [height of the object /  height of the image]  

    m = -[-4]/1

     m=4

v=???

 m= -v/u

so,

4= -v/-20

v=80

f=??

1/f = 1/v= 1/u [mirror formula]

1/f = 1/80 - 1/-20

1/f = 1-4/80

1/f= -3/80

f = 80/-3

done!!.

thank you!!.

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

Thanks

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