Question

the focal length of a concave lens is 30 cm at what distance should be the object placed from the lens so that it forms an image at 20 cm from the lens​

Answer 1

Given

f = -30 cm

v = -20 cm

u = ?

Now

1/f = 1/v - 1/u

1/-30 = 1/-20 -1/u

-1/30 = -1/20 -1/ u

-1/30 + 1/20 = -1/u

1/60 = -1/u

-1/60 = 1/u

u = -60

the distance of the object should be 60 cm from the lens

Answer 2

Given:

• Focal length = 30 cm
• Image distance = 20 cm

To find:

Object distance ?

Calculation:

Applying LEN'S FORMULA:

$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}$

• Concave lens always produces virtual image in front of lens, hence sign of 'v' will also be negative.

$\implies \dfrac{1}{ - 30} = \dfrac{1}{ - 20} - \dfrac{1}{u}$

$\implies \dfrac{1}{u} = - \dfrac{1}{20} + \dfrac{1}{30}$

$\implies \dfrac{1}{u} = \dfrac{ - 3 + 2}{60}$

$\implies \dfrac{1}{u} = \dfrac{ - 1}{60}$

$\implies u = - 60 \: cm$

So, object distance has to be 60 cm in front of lens.