Question

An object of height 4.0cm is placed at a distance of 30cm from the optical centre 'O' of a convex lens of focal length 20cm. Draw a ray diagram to find the position and size of the image formed. Mark optical centre 'O',principal focus F on the diagram. Also find ratio of size of the image to the size of the object.

Answer 1

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

Now, use formula,
1/v - 1/u = 1/f
Here, u = -30cm, f = 20cm
∴ 1/v -1/-30 = 1/20
⇒ 1/v = 1/-30 + 1/20 = (30 - 20)/20×30 = 1/60
⇒1/v = 1/60 ⇒ v = 60cm

now, we should use formula of magnification
m = v/u = height of image/height of object
Here , v = 60cm, u = -30cm, height of object = 4cm ,
so, 60cm/-30cm = height of image/4cm
-2 = height of image/4
height of image = -8cm , here negative sign shows image is formed below of optical axis { horizontal line }

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

Hence, height of image or size of image = 8cm
image distance form lens = 60cm , right side
and ratio of image size or object size is 2 {excluding sign }

ray diagram of image , its position , principal focus are shown in figure.
Where h shown height of image e.g., 8cm , v is shown distance of image from lens e.g., 60cm .

Answer 2

Answer:

height of object, h₀ = 4cm

object distance from lens , u = 30cm

Focal length of lens , f = 20cm

Now, use formula,

1/v - 1/u = 1/f

Here, u = -30cm, f = 20cm

∴ 1/v -1/-30 = 1/20

⇒ 1/v = 1/-30 + 1/20 = (30 - 20)/20×30 = 1/60

⇒1/v = 1/60 ⇒ v = 60cm

now, we should use formula of magnification

m = v/u = height of image/height of object

Here , v = 60cm, u = -30cm, height of object = 4cm ,

so, 60cm/-30cm = height of image/4cm

-2 = height of image/4

height of image = -8cm , here negative sign shows image is formed below of optical axis { horizontal line }

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

Hence, height of image or size of image = 8cm

image distance form lens = 60cm , right side

and ratio of image size or object size is 2 {excluding sign }

ray diagram of image , its position , principal focus are shown in figure.

Where h shown height of image e.g., 8cm , v is shown distance of image from lens e.g., 60cm .

Plz mark as brain list answer