Question

S.No.	Object-Distance u(cm)	Image-Distance v(cm)
1.	-100	+25
2.	-60	+30
3.	-40	+40
4.	-30	+60
5.	-25	+100
6.	-15	+120

Analyse the following observation table showing variation of image-distance (v) with object-distance (u) in case of a convex lens and answer the questions that follow without doing any calculations
What is the focal length of the convex lens? Give reason to justify your answer.

Answer 1

From the table:

When the object is placed at $40cm$ in front of the convex lens, the image is formed at $40cm$ from the lens on the other side. This means that the image formed is real and inverted. Also, here, the image distance and object distance are same; this happens when the object is placed at the centre of curvature of the lens.

We know that, $R=2f$, where $R=$ radius of curvature, $f=$ focal length of the lens.

Radius of curvature is defined as the distance from the optical centre to the centre of curvature.

Thus, here $R=40cm$

Hence, $f=\frac{R}{2}=\frac{40}{2}=20cm$

Also, from other cases:

1. When the object is placed at $100cm$ in front of the convex lens, the image is formed at $25cm$ from the lens on the other side, i.e., when the object is placed beyond the centre of curvature, the image is formed between the focus and centre of curvature on the other side of the convex lens.
   
2. When the object is placed at $60cm$ in front of the convex lens, the image is formed at $30cm$ from the lens on the other side, i.e., when the object is placed beyond the centre of curvature, the image is formed between the focus and centre of curvature on the other side of the convex lens.
   
3. When the object is placed at $30cm$ in front of the convex lens, the image is formed at $60cm$ from the lens on the other side, i.e., when the object is placed between the focus and centre of curvature, the image is formed beyond the centre of curvature on the other side of the convex lens.
   
4. When the object is placed at $25cm$ in front of the convex lens, the image is formed at $100cm$ from the lens on the other side, i.e., when the object is placed between the focus and centre of curvature, the image is formed beyond the centre of curvature on the other side of the convex lens.