Question

S.No.	Object distance(cm)	image distance(cm)
1.	60	15
2.	48	16
3.	36	21
4.	24	24
5.	18	36
6.	16	48

A student was asked by his teacher to find the image distance for various object distances in case of a given convex lens. He performed the experiment with all precautions and noted down his observations in the above table:
After checking the observation table the teacher pointed out that there is a mistake in recording the image distance in one of the observations. Find the serial number of the observation having faulty image distance.
A. $2$
B. $3$
C. $5$
D. $6$

Answer 1

Hint: In order to solve such question you should always try to find the focal length first to do that look for the data when image distance is same as object distance this case is only true when object is placed at a distance of twice the distance of the focal length.

Complete answer:
Let's find the focal length first:
As we can see in observation 4 image distance is same object distance (both are \[24cm\])
And this is only possible when object distance is twice the focal length. Therefore, \[2f = 24cm\] where $f$ is focal length.Which implies \[f = 12cm\].

Now we will use the property of image formation by a convex lens to eliminate wrong observations. When an object is placed at a distance of \[18{\text{ }}cm\] image is formed at \[36cm\]. (we can verify it using lens formula)

Now if we use principle of reversibility we can say that if object is placed at \[36cm\] then image will be formed at \[18{\text{ }}cm\] but as we can see in observation 3 it is given that image is formed at \[21cm\] which is wrong. When the object is between infinity and the centre of curvature, the image formed is between focus and centre of curvature so we can be little sure about observation 1 and observation 2.

Hence Option B is the correct answer.

Note: You don’t have to calculate the value of image distance corresponding to each object distance you can simply use analogy to solve each question like here if you use the principle of reversibility concept you can easily say that either the observation 3 or the observation 5 is wrong now you can verify either to get the correct answer.