Question

a convex lens has a focal length of 20cm .find the position of the object for which the image will be half the size of the object.​

Answer 1

Answer:

-20

Explanation:

Given:

Focal length = 20 cm

Magnification = $\dfrac{1}{2}$

To find:

• Position of the object for which magnification is $\dfrac{1}{2}$

So now using the formula:

$\frac{1}{2} = \frac{-V}{u}$

Cross multiplying:

-2V=u

$V=\dfrac{-2}{u}$

Using the other formula which says:

$\frac{1}{f} =\frac{1}{v} +\frac{1}{u}$

Focal length = f = 20 cm (given)

We derived and got $V=\dfrac{-2}{u}$

And we have to find u

$\dfrac{1}{20} = \dfrac{-2}{u} + \dfrac{1}{u}$

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

u = -20 cm

It has to be placed at a position of 20 cm for the image  to be half size of the object

Answer 2

Given :

• Focal length of Convex lens is 20 cm
• Magnification is -1/2

To Find :

• Object Distance when magnification is 1/2

Solution :

Use formula for magnification of lens :

➠ m = -v/u

⇒1/2 = -v/u

⇒-v = u/2

⇒v = -u/2 ...(1)

___________________________

Now, use lens formula :

➠1/f = 1/v + 1/u

⇒1/20 = 1/-u/2 + 1/u

⇒1/20 = -2/u + 1/u

⇒1/20 = -1/u

⇒-u = 20

⇒u = - 20

$\therefore$ Object is placed at distance of 20 cm from lens, negative sign indicates that object is placed on left side of lens .