A student performed the experiment of determination of focal length of a concave mirror by (u-v) method using an optical bench of length `1.5m`. 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),(60,33),(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)`.

Options

A. `(42,560`
B. `(48,48)`
C. `(66,33)`
D. `(78,39)`

Answer

C, D

Explanation

`(1)/(v)+(1)/(u)=(1)/(f)` or `(1)/(-|v|)+(1)/(-|u|)=(1)/(-|f|)rArr |v|=(|u||f|)/(|u|-|f|)`
For `|u|=42,|f|=24 ,|v|=((42)(24))/(42-24)=56 cm` so `(42,56)` is correct observation
For `|u|=48` or `|u|=2f` so `(48,48)` is correct observation
`|v|=((66)(24))/(66-24)~~36 cm` which is not in the permissible limit
so `(66,33)` , is incorrect recorded
For `|u|=78, |f|=24 cm`
`|v|=((78)(24))/(78-24) ~~32 cm` which is also not in the permissible limit.
so `(78,39)` , is incorrect recorded.