Question

14. You are provided with a concave lens having
focal length 15 cm. If it diminishes the image by
one third, calculate the distance of image from
lens.​

Answer 1

Answer:

10 cm

Explanation:

f = +15 cm

m = 1/3

since, m = v/u

hence, 1/3 = v/u

now, u = 3v

since, 1/v = 1/f + 1/u

= 1/v = 1/15 + 1/3v (u = 3v)

= 1/v = (v+5)/15v

= 15 = v+5

therefore,. v = 10cm

Hope this helps.

Answer 2

Given:

The focal length of the lens = 15 cm

The image is diminished by one third

To Find:

The distance of the image from  lens (v)

Solution:

The distance of the image from  the lens is -10 cm.

Given that the image is 1/3 the size of the object

Using magnification formula for a lens, m = hi / ho = v / u

or v / u = 1 / 3      - (1)

Using the lens formula,

1/f = 1/v - 1/u

Substituting f = - 15 cm

$\frac{-1}{15} = \frac{u-v}{uv}$

or u v = 15 v - 15 u

Substituting u = 3v

3v² = 15v - 15 (3v)

or 3v = 15 - 45

or v = -30/3

or v = - 10 cm