Question

If an object of height 2cm is placed 12cm away from converging lens of 8cm focal length then find the nature,height and image distance​

Answer 1

GIVEN:- 1. height of the object is 2cm.

2. lens is converging or convex lens.

3. u = -12cm.

4. f = 8cm. ( using sign convention for convex lens )

To find :- nature of the image, height of the image and v = ?

Explanation:-

using lens formula,

1/f = 1/v - 1/u

=> 1/8 = 1/v - 1/-12

=> 1/8 = 1/v + 1/12

=> 1/v = 1/8 - 1/12

=> 1/v = 1/24

=> v = 24 cm.

so, v = 24 cm.

hence, image distance is 24 cm from the lens.

Now,

because 'v' is positive, so image be real.

After this, we have to calculate height of the image.

so, using magnification formula,

m = hi/ho = v/u

=> hi/ho = v/u

=> hi = v • ho/ u

=> hi = 24 • 2/-12

=> hi = -2 • 2

=> hi = -4.

here, height of the image is negative.

so, image be inverted.

here, hi > ho

so, image is enlarged.

Hence, the image is formed at the distance of 24cm from the lens. The image is real, inverted and enlarged. The height of the image is 4cm.

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