Question

An object of size 1.5cm is placed at a distance of 15cm from a convex lens.

An image is formed at 30cm from the lens. Calculate the
(i) size of the image and its nature
(ii) power of the lens​

Answer 1

Given:-

• Object -height ,ho = 1.5 cm

• Object distance ,u = 15cm

• Image - distance ,v = 30cm

To Find:-

• (i) size of the image and its nature .

• (ii) power of the lens.

Solution:-

Firstly we calculate the focal length of lens

Using lens Formula

• 1/v - 1/u = 1/f

Substitute the value we get

→ 1/f = 1/30 -1/(-15)

→ 1/f = 1/30 +1/15

→ 1/f = 1+2/30

→ 1/f = 3/30

→ 1/f = 1/10

→ f = 10cm

Therefore, the focal length of the lens is 10cm.

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[ii]

Power of Lens is defined as the reciprocal of its focal length .

• P = 1/f (in metre)

Substitute the value we get

→ P = 1/10/100

→ P = 100/10

→ P = 10 D

Therefore, the Power of the lens is 10 Dioptre.

Now, Using magnification Formula

•m = hi/ho = v/u

Substitute the value we get

→ hi/1.5 =-30/15

→ hi/1.5 = -2

→ hi = -1.5×2

→ hi = -3 cm

Therefore , the height of the image is 3 cm

The image formed by the lens is Real and Inverted.