Question

A 2.5 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 15cm. The distance of the object from the lens is 30cm .Find the position and the size of the image.​

Answer 1

Given :-

Height of Object = O = 2.5 cm

Focal length = f = 15 cm

Object distance = u = -30 cm

Using Lens Formula,

1/v - 1/u = 1/f

1/v - (-1/30) = 1/15

1/v = 1/15 - 1/30

1/v = 2-1/30

v = 30 cm

Again,

m = I/O = v/u

I/2.5 = 30/-30

I = -2.5 cm

Hence,

From this we conclude that Height of Image is same as height of Object.

Answer 2

Explanation:

Given :-

A 2.5 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 15cm. The distance of the object from the lens is 30cm

To Find :-

Position

Size

Solution :-

We know that

1/f = 1/v - 1/u

1/15 = 1/v - 1/(-30)

1/15 = 1/v - (-1/30)

1/15 = 1/v + 1/30

1/15 - 1/30 = 1/v

2 - 1/30 = 1/v

1/30 = 1/v

30 × 1 = 1 × v

30 = v

Now

m = hi/ho = v/u

hi/2.5 = 30/-30

hi/2.5 = -1

hi = 2.5 × (-1)

hi = -2.5 cm

Position :- Real, inverted and diminished