Question

41. A convex lens forms 19 times magnified image of an
object on a screen placed 10 m from the lens. What is
the focal length of the lens?
Ans. 0.5 m.
.
1
-1
1
.
1

Answer 1

$\huge{\boxed{\boxed{\mathfrak{\underline{Solution:}}}}}$

$\large{\bf{\underline{\underline{Given:-}}}}$

=> Magnification = -19

=> v = 10 m

$\large{\bf{\underline{\underline{To\;Find:-}}}}$

=> Focal Length.

$\large{\bf{\underline{\underline{Formula\;used:-}}}}$

$\sf{\implies \dfrac{1}{f}=\dfrac{1}{v} - \dfrac{1}{u} \;\;\;\;\;[Lens\;Formula]}$

So,

$\sf{\implies Magnification = \dfrac{v}{u}}$

$\sf{\implies -19=\dfrac{10}{u}}$

${\boxed{\boxed{\sf{\implies u = - \dfrac{10}{19}\;m}}}}$

Now, By using Lens Formula,

$\sf{\implies \dfrac{1}{f}=\dfrac{1}{v} - \dfrac{1}{u} \;\;\;\;\;[Lens\;Formula]}$

$\sf{\implies \dfrac{1}{f} =\dfrac{1}{10}-\Bigg(\dfrac{1}{-\frac{10}{19}}\Bigg)}$

$\sf{\implies \dfrac{1}{f} =\dfrac{1}{10}+\dfrac{19}{10}}$

$\sf{\implies \dfrac{1}{f} =\dfrac{20}{10}=2}$

${\boxed{\boxed{\sf{\implies f = \dfrac{1}{2}=0.5\;m}}}}$

So, Focal length of lens is 0.5 m.