Question

an object of height 4 cm is placed at a distance of 30 cm from the optical centre of the convex lens of focal length 20 cm. find the position and size of the image and also find appropriate ratio of size of the image to the size of the object

Answer 1

convex lens
h = 4cm
u = -30cm
f = +20cm
1/f = 1/v - 1/u
1/20 = 1/v - 1/-30
1/20 1/v + 1/30
1/20 - 1/30 = 1/v
3-2
----- = 1/v
60
1/60 = 1/v
60cm = v

h'/h = v/u
h'/4 = 60/-30
h' = 4×-2
h' = -8

ratio = 1:2

size: enlarged
position: beyond 2F2

Answer 2

height of object , h₀ = 4cm
object distance from centre of lens, u = 30cm
focal length , f = 20cm

Now, use lens formula,
1/v - 1/u = 1/f
Here, u = -30cm , f = 20cm
⇒1/v - 1/-30cm = 1/20cm
⇒ 1/v = 1/20 - 1/30 = (30-20)/20 × 30 = 1/60
v = 60cm
Hence, image is formed at 60cm right side of lens

Now, we should use magnification concept
m = v/u = height of image/height of object
60cm/-30cm = h/h₀ = h/4cm
⇒ -2 = h/4cm, h = -8cm, here negative sign shows that image is forming below the optical axis.

Now, ratio of image size/object size = 8cm/4cm {excluding sign} = 2