Question

An object 2 cm high is placed at a distance of 25 cm from the optical centre of a concave lens of focal lengur
15 cm. Calculate
(a) the position of the image (b) the size of the image.​

Answer 1

Answer:

Explanation:

Solution,

Here, we have

Object height, h₁ = 2 cm

Object distance, u = - 25 cm

Focal length, f = - 15 cm

To Find,

(a) The position of the image, v = ?

(b) The size of the image, h₂ = ?

According to the Lens Formula,

We know that

1/v = 1/f + 1/u

So, putting all the values, we get

1/v = 1/f + 1/u

⇒ 1/v = 1/- 15 + 1/- 25

⇒ 1/v = 1/- 15 - 1/25

⇒ 1/v = - 5 - 3/75

⇒ 1/v = - 8/75

⇒ v = - 75/8

⇒ v = - 9.37 cm

Hence, the position of the image is - 9.37 cm.

Now, According to the magnification formula,

We know that,

m = v/u = h₂/h₁

So, putting all the values again, we get

⇒ v/u = h₂/h₁

⇒ - 75/-25 × 8 = h₂/2

⇒ h₂ = 3/8 × 2

⇒ h₂ = 3/4

⇒ h₂ = 0.75 cm

Hence, the size of the image is 0.75 cm.