Question

If an object is 30 cm in front of a convex mirror that had a focal length of 60 cm , how far behind the mirror will the image appear to an observer ?How tall will the image be ?​

Answer 1

Given :

• position of object , u = -30 cm
• focal length of convex mirror , f = 60 cm

To find :

• position of image
• Magnification of image

Formula needed :

• Mirror formula

      1/f = 1/v + 1/u

• formula for Magnification

      m = -v / u

Solution :

Calculating position of image

Using mirror formula

→ 1/f = 1/v + 1/u

→ 1/60 = 1/v + 1/(-30)

→ 1/v = 1/60 + 1/30

→ 1/v = ( 1 + 2 ) / 60

→ 1/v = 3/60

→ v = 20 cm

Therefore,

position of image is 20 cm behind the mirror .

Calculating magnification of image

Using formula

→  m = -v / u

→  m = -20 / -30

→ m = 2/3 = 0.67

Therefore,

Image formed will be smaller in size than size of object by a factor of 0.67

( image formed will be virtual and erect )

Answer 2

Answer: V=20cm and m=2/3

Explanation:

u=-30cm

f=60cm

using mirror formula,1/v+1/u=1/f

1/v+1/-30=1/60

1/v=1/30+1/60

v=60*60/60+30

v=60*30/90

v=20cm

Now,

        m=-v/u

         m=-20/-30

         m=2/3

          m=0.67