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 4 sets of (u, v) values recorded by the student(in cm) are: (42, 56), (48, 48), (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)
• D. (78, 39)

Answer 1

Answer: (C), (D)

The correct options are
C (66, 33)
D (78, 39)

For the given concave mirror: $f=-24cm$

Mirror formula is $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

so, $v=\frac{uf}{u-f}$

Case 1: $u=-42cm$,

$v=\frac{-24\times (-42)}{-42+24}=-56cm$

Satisfies

Case 2: $u=-48cm$

$v=\frac{-24\times (-48)}{-48+24}=-48cm$

Satisfies

Case 3: $u=-66cm$

$v=\frac{-24\times (-66)}{-66+24}=-37.71cm$

Does not satisfy

Case 4: $u=-78cm$

$v=\frac{-24\times (-78)}{-78+24}=-34.66cm$

Does not satisfy

Therefore incorrectly recorded data set are (66,33) and (78, 39)

Answer. C (66,33) and D (78,39)