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) Focal Length of the Convex Lens

`1/f = 1/v + 1/u`

From the given table, the observation at Sr. No. 3 (u = −50 cm, v = +50 cm) clearly indicates that the object is placed at twice the focal length (2f) because the image distance equals the object distance, meaning the image is real, inverted, and of the same size as the object. This happens only when the object is at 2f. Therefore:

`f = (50  cm)/2`

= 25 cm

2) Incorrect Observation

• The 6th observation (u = −15 cm, v = +37.5 cm) is not correct.
• Reason: For a convex lens, when the object is placed within the focal length (u < f), the image should be virtual, erect, and on the same side as the object (with a positive image distance). However, this observation shows a real image with a positive image distance, which is not possible.

3) Magnification for u = −30 cm

`M = -v/u`

• u = −30 cm
• v = +150 cm

`M = -(150/-30)`

= −5

This means the image is 5 times larger than the object, real, and inverted.