Question

The variation of image distance (v) with object distance (u) for a convex lens is given in the following observation table. Analyse it and answer the questions that follow:

Sr. No.	Object distance (u) cm	image distance (v) cm
1	-150	+30
2	-75	+37.5
3	-50	+50
4	-37.5	+75
5	-30	+150
6	-15	+37.5

1. Without calculation, find the focal length of the convex lens. Justify your answer.
2. Which observation is not correct? Why? Draw ray diagram to find the position of the image formed for this position of the object.
3. Find the approximate value of magnification for u = – 30 cm.

Answer 1

1. The focal length of the convex lens can be found at the object distance where the image distance is equal but with an opposite sign, indicating that the object is at the centre of curvature (2F) and the image is also formed at the centre of curvature on the opposite side (2F). In the table, this situation occurs for the entry where u = -30 cm and v = +30 cm; hence, the focal length (F) is half of this distance, meaning the lens's focal length is 15 cm.

2. We look for an inconsistency with the lens formula 1/f = 1/u + 1/v to find which observation is incorrect. Here, without calculation, we could look for a pattern that doesn't align with the expected behaviour of a convex lens, such as an image distance being lesser than the object distance for real images. A discrepancy in this pattern would suggest an incorrect observation. Determining the exact position without calculation is not feasible as it requires either a calculation or a construction of a ray diagram, which cannot be drawn in this format.

3. The magnification (m) is given by the formula m = −v/u. For u = –30 cm, v is given as + 150 cm, therefore = −150/−30 = 5m = −150/−30 = 5. The approximate magnification value for u = –30 cm is 5, indicating that the image is magnified 5 times larger than the object.