Question

A needle 4 cm high is placed in front of a lens. Image of the needle is real ,inverted and 6 cm high , when distance between the needle and its image is 20 cm. Find the focal leght of lens and also write the type if this lens.

Answer 1

h = 4cm

h' = -6cm

u + v = 20cm eq. no.1

h'/h = v/u

-6/4 = v/u

v = -6u/4 eq. no.2

substituting 2nd equation in 1st we get,

u -6u/4 = 20

(4u - 6u) / 4 = 20

-2u = 80

u = -40 eq. no. 3

substituting eq. no . 3 in 1st we get,

-40 + v = 20

v = 60

now, 1/f = 1/v - 1/u

1/f = 1/60 - 1/-40

1/f = 1/60 + 1/40

1/f = 2/120 + 3/120

1/f = 5/120

1/f = 1/24

f = 24

So the focal length is 24 cm

Since f is positive, it is a convex lens...

Hope u got it..

and its a nice question.. :)