Question

A two times larger, virtual image is formed of an object placed at a distance of 20 cm from a lens. Find the distance of the image and focal length of the lens.

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

A two times larger,virtual image is formed of an object placed at a distance of 20 cm from a lens.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The distance of the image and focal length of the lens.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

We have;

• Distance of object from lens (u) = -20 cm
• Magnification (m) = 2

We know that formula of the magnification :

$\boxed{\bf{Magnification=\frac{v}{u} }}}$

A/q

$\longrightarrow\rm{2=\dfrac{v}{-20} }\\\\\longrightarrow\rm{-40=v}\\\\\longrightarrow\rm{\pink{v=-40\:cm}}$

We know that formula of the lens :

$\boxed{\bf{\frac{1}{f}=\frac{1}{v}-\frac{1}{u} }}}$

$\longrightarrow\rm{\dfrac{1}{f} =-\dfrac{1}{40} -\dfrac{1}{(-20)} }\\\\\\\longrightarrow\rm{\dfrac{1}{f} =-\dfrac{1}{40} +\dfrac{1}{20}}\\\\\\\longrightarrow\rm{\dfrac{1}{f} =\dfrac{-1+2}{40} }\\\\\\\longrightarrow\rm{\dfrac{1}{f} =\dfrac{1}{40} }\\\\\\\longrightarrow\rm{\pink{f=40\:cm}}$

∴ Image will be formed at the distance of 40 cm on the side as the object and the focal length of the lens will be 40 cm.