A student performed the experiment of determination of focal length of a concave mirror by 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

Question

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) [2009]

(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) [2009]

Smart Achievers · Accepted Answer

(3, 4)

$Given f = - 24 cm$

Applying mirror formula, $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

The $u - v$ values of options (1) and (2) match with mirror formula, whereas options (3) and (4) do not match with mirror formula.

For $(66, 33)$ ,

$\Rightarrow \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{- 24} + \frac{1}{66} = \frac{- 66 + 24}{24 \times 66} = \frac{- 42}{24 \times 66}$

$\Rightarrow v = - \frac{24 \times 66}{42} = - 37.7 cm$

But the value of $v = 33 cm$ . The absolute error is $37.7 - 33 = 4.7 cm,$ which is greater than $0.2 cm$ . Therefore, it is a wrong reading. For $(78, 39)$ , when $u = 78$ , then

$\frac{1}{v} + \frac{1}{- 78} = \frac{1}{- 24}$ $\Rightarrow v = - 34.67 cm$

The absolute error is $39 - 34.67 = 4.33 cm,$ which is greater than $0.2 cm$ .

Solution

1 (42, 56)

2 (48, 48)

3 (66, 33)

4 (78, 39)

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