Question

A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length of 15 cm. Find the nature of the image formed.

Answer 1

Heya mate
The answer is here







Height of the needle (h1) = 4.5 cm

Object distance( u) = – 12 cm

Focal length of the convex mirror (f)= 15 cm

Image distance = v

The value of v can be obtained using the mirror formula:

1/f = 1/v - 1/u

1/u = 1/v - 1/f

= 1/-25 - 1/5

= -5 -1/25

= -6/25

u = -25/6 = -4.167 cm

1/v = 1/f - 1/u

1/f = 1/u + 1/v

= 1/15 + 1/12

= 4 +5/60

= 9/60

f = 60/9 = 6.7 cm

Hence, the image of the needle is 6.7 cm away from the mirror. Also, it is on the other side of the mirror.

The image size is

m = h2/h1 = -v/u

h2 = -v x h1 /u

= -6.7 x 4.5/ -12 = 2.5 cm

The positive sign indicates that the image is erect, virtual, and diminished.




hope it helps