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JEE Advance - Physics (2009 - Paper 1 Offline - No. 11)

A student performed the experiment of determination of focal length of a concave mirror by $$u$$-$$v$$ method using an optical bench of length 1.5 m. The focal length of the mirror used is 24 cm. The maximum error in the location of the image can be 0.2 cm. The 5 sets of ($$u,v$$) values recorded by the student (in cm) are : (42, 56), (48, 48), (60, 40), (66, 33), (78, 39). The data set(s) that cannot come from experiment and is (are) incorrectly recorded, is (are)
(42, 56)
(48, 48)
(66, 33)
(78, 39)

Explication

Using mirror formula for the concave mirror, we have

$${1 \over v} + {1 \over u} = {1 \over f}$$

Option (A) : When the value is (42, 56), we have

$${1 \over { - 56}} + {1 \over { - 42}} = {{ - 98} \over {56 \times 42}} \Rightarrow f = {{ - 56 \times 42} \over {98}} = - 24$$ cm

Option (B) : When the value is (48, 48), we have

$${1 \over { - 48}} + {1 \over { - 48}} = {{ - 1} \over {24}} \Rightarrow f = - 24$$ cm

Option (C) : When the value is (66, 33), we have

$${1 \over { - 33}} + {1 \over { - 66}} = {{ - 1} \over {22}} \Rightarrow f = - 22$$ cm

Option (D) : When the value is (78, 39), we have

$${1 \over { - 39}} + {1 \over { - 78}} = {{ - 1} \over {26}} \Rightarrow f = - 26$$ cm

Since options (A) and (B) give $$f = - 24$$ cm, which is the same as that given in the problem, we conclude that the options (C) and (D) as the correct options.

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