Question

A real image 2/3rd of the size of an object is formed by a convex lens when the object is at a distance of 12cm from it. Find the focal length of the lens.

Answer 1

$\mathtt{\bf{\huge{\underline{\red{Given :- }}}}}$

• A real image = 2/3rd of the size of an object.

• It is formed by a convex lens when the object is at a distance of 12cm from it.

$\mathtt{\bf{\huge{\underline{\green{To\:Find :- }}}}}$

• The focal length of the lens.

$\mathtt{\bf{\huge{\underline{\pink{Solution :- }}}}}$

According to the question,

v = 12 cm

Size of image = -2/3 × size of object.

We know that ,

Magnification = $\dfrac{size\:of\:image}{size\: of \:object}$

➝ $\dfrac{v}{u}$

➝ -2/3 = $\dfrac{v}{u}$

➝ u = -1.5v

The object distance (u ) = -1.5v = -1.5 × 12 = -18cm

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

➝ $\dfrac{1}{12}$ - $\dfrac{1}{-18}$ = $\dfrac{1}{f}$

➝ $\dfrac{1}{12}$ + $\dfrac{1}{18}$ = $\dfrac{1}{f}$

➝ $\dfrac{1}{f}$ = $\dfrac{5}{36}$

➝ f = 7.2 cm

Hence, the focal length of the lens is 7.2 cm.

______________________________________

Answer 2

Answer:

A real image = 2/3rd of the size of an object.

It is formed by a convex lens when the object is at a distance of 12cm from it.

$\mathtt{\bf{\huge{\underline{\green{To\:Find :- }}}}}$

The focal length of the lens.

$\mathtt{\bf{\huge{\underline{\pink{Solution :- }}}}}$

According to the question,

• v = 12 cm
• Size of image = -2/3 × size of object.

We know that ,

Magnification = $\dfrac{size\:of\:image}{size\: of \:object}$

➝ $\dfrac{v}{u}$

➝ -2/3 = $\dfrac{v}{u}$

➝ u = -1.5v

The object distance (u ) = -1.5v = -1.5 × 12 = -18cm

➝ $\dfrac{1}{v}$

=$\dfrac{1}{u}$

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

➝ $\dfrac{1}{12}$

$- \dfrac{1}{-18}$

= $\dfrac{1}{f}$

➝ $\dfrac{1}{12}$

=$\dfrac{1}{18}$

= $\dfrac{1}{f}$

➝ $\dfrac{1}{f}$

= $\dfrac{5}{36}$

➝ f = 7.2 cm

• Hence, the focal length of the lens is 7.2 cm.