Question

The refractive index of water measured by the relation $\mu =\frac{\text{ real depth }}{\text{ apparent depth }}$ is found to have values of 1.34, 1.38, $1.32$ and $1.36$; the mean value of refractive index with percentage error :-

• A. $1.35\pm 1.48\%$
• B. $1.35\pm 0\%$
• C. $1.36\pm 6\%$
• D. $1.36\pm 0\%$

Answer 1

Answer: (A)

The mean value of refractive index,
$\mu =\frac{1.34+1.38+1.32+1.36}{4}=1.35$
and
$\Delta \mu =\frac{|(1.35-1.34)|+|(1.35-1.38)|+|(1.35-1.32)|+|(1.35-1.36)|}{4}$
$=0.02$
Thus $\frac{\Delta \mu }{\mu }\times 100=\frac{0.02}{1.35}\times 100=1.48\%$