Question

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

S. 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 out the focal length of the given convex lens. Justify your answer.  1
2. Which one of the observations given in the table is not correct and why?  1
3. 1. Find out the value of magnification for u = −30 cm. Write the nature of the image formed. Give reason for your answer.  2
   2. Analyse the data given in the table above and draw the labelled ray diagram for u = −30 cm and v = 150 cm.  2

Answer 1

(a) From the table, observe:

When u = –50 cm, v = +50 cm

For a convex lens, when object distance = image distance (in magnitude), the object is at 2f.

So,

2f = 50 ⇒ f = 25 cm

(b) Use the lens formula:

`1/f = 1/v - 1/u`

Checking the last entry: u = –15 cm, v = +37.5 cm

`1/v - 1/u = 1/37.5 - (1/-15)`

= `1/37.5 + 1/15`

= `(2 + 5)/75`

= `7/75`

f = `75/7` ≈ 10.7 cm (not 25 cm)

This does not match the focal length. It does not satisfy the lens formula for f = 25 cm.

(c) (i)

Given:

u = −30
v = +150

`m = v/u = 150/-30 = -5`

Nature of image:

• Negative magnification → Real and inverted
• Magnitude > 1 → Enlarged

(c) (ii)