JEE Advanced · 2009 · 12 Apr 2009 · Paper 1 · Geometrical Optics

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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 meter. 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)

(A) $(42, 56)$
(B) $(48, 48)$
(C) $(66, 33)$ ✓ Correct
(D) $(78, 39)$ ✓ Correct

Answer: (C), (D)

Solution

Using the mirror formula

\frac{1}{f} = \frac{1}{v} + \frac{1}{u}

with

f = - 24

cm (concave mirror), we check each pair. For (42, 56):

\frac{1}{f} = \frac{1}{56} + \frac{1}{- 42} = \frac{3 - 4}{168} = - \frac{1}{168}

, so

f \approx - 168

cm (incorrect, but within error). For (48, 48):

\frac{1}{f} = \frac{1}{48} + \frac{1}{- 48} = 0

(incorrect). For (60, 40):

\frac{1}{f} = \frac{1}{40} + \frac{1}{- 60} = \frac{3 - 2}{120} = \frac{1}{120}

, so

f = 120

cm (incorrect). For (66, 33):

\frac{1}{f} = \frac{1}{33} + \frac{1}{- 66} = \frac{2 - 1}{66} = \frac{1}{66}

, so

f = 66

cm (far from 24 cm). For (78, 39):

\frac{1}{f} = \frac{1}{39} + \frac{1}{- 78} = \frac{2 - 1}{78} = \frac{1}{78}

, so

f = 78

cm (far from 24 cm). The sets (66, 33) and (78, 39) are most inconsistent with

f = 24

cm.

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JEE Advanced · 2009 · 12 Apr 2009 · Paper 1 · Geometrical Optics

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