Question

A convex lens forms an image at 30 cm from lens on a screen.if the focal length of lens is 20 cm, find the distance at which the object is placed

Answer 1

Given :

• A concave mirror forms an image at 30 cm
• Focal length of lens is 20 cm

To Find :

The distance at which the object is placed

Theory :

${\red{\boxed{\large{\bold{Lens\:Formula}}}}}$

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

Solution :

We have

$\sf\:v=30cm(by\:sign\:convention)$

$\sf\:f=20cm(by\:sign\:convention)$

and $\sf\:u=?$

Now By using Lens Formula

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

Put the given values

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

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

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

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

$\sf\implies\:u=-60cm$

Therefore, Object should be place at a distance of 60 cm on the left side of the convex lens.

Answer 2

$\dagger\mathbb\red{QUESTION: }$

A convex lens forms an image at 30 cm from lens on a screen.if the focal length of lens is 20 cm, find the distance at which the object is placed

$\dagger\mathbb\purple{SOLUTION : -60 }$

Given:

• image distance of convex lens = 30cm
• Focal length of the lens = 20cm

To find:

• object distance = ?

step by step explanation:

we have :

f = 30 , v = 20 and u = ?

to find u we need to:

$\bigstar$${\green{\underline{\mathrm{\blue{formula \: = \frac{1}{f} = \frac{1}{v} - \frac{1}{u} }}}}}$

$\sf \red{\frac{1}{30} = \frac{1}{20} - \frac{1}{u}}$

$\sf \red{ \frac{1}{u} = \frac{1}{20} - \frac{1}{30}}$

$\sf \red{ \frac{1}{u} = \frac{20 - 30}{30 \times 20} }$

$\sf \red{ \frac{1}{u} = \frac{ - 10}{600} }$

$\sf \red{ \frac{1}{u} = \frac{ - 1 {\cancel{0}}}{60 {\cancel{0}}} }$

$\sf \red{ {u} = - 60 }$

Therefore:

Object should be place at a distance of 60 cm on the left side of the convex lens.