Question

Calculate the focal length of a convex lens which produces a virtual image at a distance of $50cm$ of an object placed $20cm$ in front of it.

Answer 1

Hint:Firstly we have to figure out all the known quantities for the given question ( In this case the image distance and the object distance ). Then we have to give the correct formula to find the focal length when both the image and object distance is known. Then we can put the values in the equation accordingly th sign convention and we can get the correct answer.

Complete step by step answer:
Firstly we have to sort out what we have got :
The distance of the image from the lens is : $v = 50cm$
 The distance of the object from the lens is : $u = 20cm$
Step 1: Firstly we have to define the formula for the interrelation for the image distance and the object distance which is :
$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}$

Step 2: Since the image is virtual and formed on the same side of the object, therefore the signs would be respectively negative. Then we have all the values so we can find the focal length by putting the values and solving the equation :
\[
  \dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u} \\
  \dfrac{1}{f} = \dfrac{1}{{ - 50}} - \dfrac{1}{{ - 20}} \\
  \dfrac{1}{f} = \dfrac{{ - 2 + 5}}{{100}} \\
  \dfrac{1}{f} = \dfrac{3}{{100}} \\
 \]
Therefore the focal length would be :
$f = \dfrac{{100}}{3}cm$

Note: There is a specific sign convention defined for the given kind of the system. In that when the object is placed in front and the left side, then all the distances to the right of the lens or mirror are positive and the distances to the left are negative. Similarly the distance above the axis is positive and below it is negative.