Question

Rena and Vani find a discarded plastic lens lying on the beach. The girls discuss what they learnt in Physics and argue whether the lens is a converging or diverging one. When they look through the lens, they notice that the objects are inverted.
(i) If an object 25cm in front of the lens forms an image 20cm behind the lens, what is the focal length of the lens?
(ii) Is it a converging or diverging lens?

Answer 1

In this question, our concept of the lens formula is tested as well as the properties of image formed when kept in front of a lens. We should take the data given in the question and use the lens formula to find the focal length of the lens.

Complete step by step answer:
According to the given values given in the question, we can see:
The distance of the object from the lens (u) = 25cm
The distance of the image from the lens (v) = 20cm
Now when we apply these values to the lens equation, we must follow the sign convention of the lens equation. The sign convention states that
All distances have to be considered from pole of the lens to the object or image,
Hence, the object distance(u) = -25cm
And the image distance(v) = +20cm.
Now we will put the values in the lens equation.
The lens equation states,
$\dfrac{1}{f} = \dfrac{1}{v}\, - \,\dfrac{1}{u}$
Now we put the values with sign convention,
$\Rightarrow\dfrac{1}{f} = \dfrac{1}{{20}}\, - \,\dfrac{1}{{ - 25}}\\\ \Rightarrow\dfrac{1}{f} = \dfrac{5}{{100}}\, + \dfrac{4}{{100}}\\\ \Rightarrow\dfrac{1}{f} = \dfrac{9}{{100}}\\\ \therefore f = 11.11\,\rm{cm}$
The focal length of the lens found by Reena and Vani is 11.11cm.
Now the question is which type of lens is it?
As we have the information that Reena and Vani have seen through the lens and have seen that the objects are seen inverted through the lens. Real inverted images are produced by convex lenses.
A convex lens is a converging lens. Therefore, the lens is a convex lens.

Note: The sign convention is to be considered and applied very carefully, the rays which are in direction of incident rays should be taken positive and the rays opposite to the incident rays should be taken negative. And all the distance measured should be from the pole of the lens.