Question

Write the serial number of the observation which is not correct. On what basis have you arrived at this conclusion?

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 $40cm$ in front of the convex lens, the image is formed at $40cm$ from the lens on the other side, i.e., when the object is placed at the centre of curvature, the image is formed at the centre of curvature of the lens on the other side.
   
4. 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.
   
5. 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.
6. When the object is placed at $15cm$ in front of the convex lens, the image has to be formed at $120cm$ from the lens on the same side of the lens, i.e., when the object is placed between the focus and the optical centre, the image is formed beyond the centre of curvature on the same side of the convex lens. But, in the table the sign of the image distance is positive, which means the image is formed on the other side, which is wrong. The sign has to be positive (same sign as the object distance).

Thus, the serial number $6$ is not correct.