Question

Calculate the distance at which an object should be placed in front of a convex lens of focal length 100 cm to obtain an error image of double its size.

Answer 1

Answer: The object should be placed at 50 cm away  from the convex lens.

Explanation:

Given that,

Focal length f = 100 cm

Magnification m= 2

The magnification is

$m = \dfrac{v}{u}$

$2 = \dfrac{v}{u}$

$v = 2u$....(I)

Using lens's formula

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

Put the value of v from equation(I)

$\dfrac{1}{100}=\dfrac{1}{2u}-\dfrac{1}{u}$

$2u = -100$

$u = -50 cm$

Hence, The object should be placed at 50 cm away  from the convex lens.

Answer 2

Answer:

Explanation:

Given :-

f = 100 cm

To Find :-

u = ??

Solution :-

m = u/u

m = 2

v = 2 u

Using 1/f = 1/v + 1/u, we get

⇒ 1/100 = 1/2u - 1/u

⇒ 1/100 = 1 - 2/2u

⇒ 1/100 = - 1/2u

⇒ 2u = - 100

⇒ u = - 100/ - 50

⇒ u = 50 cm

Hence, the distance at which an object should be placed is 50 cm.