A student was asked by his teacher to find the image distance for various object distances in case of a given convex lens. He performed the experiment with all precautions and noted down his observations in the following table:<p></p> <table> <thead> <tr> <th>S. No.</th> <th>Object distance(cm)</th> <th>Image distance(cm)</th> </tr> </thead> <tbody><tr> <td>1</td> <td>60</td> <td>15</td> </tr> <tr> <td>2</td> <td>48</td> <td>16</td> </tr> <tr> <td>3</td> <td>36</td> <td>21</td> </tr> <tr> <td>4</td> <td>24</td> <td>24</td> </tr> <tr> <td>5</td> <td>18</td> <td>36</td> </tr> <tr> <td>6</td> <td>16</td> <td>48</td> </tr> </tbody></table> <p>After checking the observation table the teacher pointed out that there is a mistake in recording the image distance in one of the observations. Find the serial number of the observation having faulty image distance.</p>

S. No.	Object distance(cm)	Image distance(cm)
1	60	15
2	48	16
3	36	21
4	24	24
5	18	36
6	16	48

Using lens formula : 1/v - 1/u = 1/f
For observation 2 :
u = -48cm
v = 16cm
∴ 1/16 - 1/(-48) = 1/f ⇒ f = 12cm
For observation 3 :
u = -36cm
v = 21cm
∴ 1/21 - 1/(-36) = 1/f ⇒ f = 13.3cm
For observation 5 :
u = -18cm
v = 36cm
∴ 1/36 - 1/(-18) = 1/f ⇒ f = 12cm
For observation 6 :
u = -16cm
v = 48cm
∴ 1/48 - 1/(-16) = 1/f ⇒ f = 12cm
Thus focal length of the lens calculated for observation 3 comes out to be different among all other observations, hence observation 3 has faulty image distance.

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