Question

a dentist uses a mirror in front of a decayed tooth at a distance of 4cm from the tooth to get a 4 times magnified image. use mirror formula to find the focal length and nature of mirror used. what is the nature of image.

Answer 1

object distance, u = -4 cm
magnification, m= 4
we know, m = -v/u ⇒ v = -mu ⇒ v = -(4)(-4) = 16 cm
so image distance= 16 cm
now, by mirror formula ,
   1/v + 1/u = 1/f
⇒ 1/16 + 1/-4 = 1/f
⇒ (1-4)/16 = 1/f
⇒ 1/f = -3/16
∴ focal length = -5.33 cm
only a concave mirror can form magnified images.
since the image is formed behind the mirror, it is virtual and erect
 

Answer 2

Answer:    object distance, u = -4 cm

magnification, m= 4

we know, m = -v/u ⇒ v = -mu ⇒ v = -(4)(-4) = 16 cm

so image distance= 16 cm

now, by mirror formula ,

  1/v + 1/u = 1/f

⇒ 1/16 + 1/-4 = 1/f

⇒ (1-4)/16 = 1/f

⇒ 1/f = -3/16

∴ focal length = -5.33 cm

only a concave mirror can form magnified images.

since the image is formed behind the mirror, it is virtual and erect