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 a reason for your answer.  (2)
      OR
   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 = `50/2`

f = 25 cm

Therefore, the focal length of the convex lens is 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 and v = +150

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

The negative sign of magnification (m = −5) indicates that the image is real and inverted, while the magnitude greater than 1 (5 > 1) confirms that the image is enlarged.

OR

(ii)