Question

The refractive index of water measured by the relation μ = $\frac{real \ depth}{apparent \ depth}$ is found to have values of 1.34, 1.38, 1.32 and 1.36; the mean value of refractive index with percentage error is
(a) 1.35 ± 1.48 %
(b) 1.35 ± 0 %
(c) 1.36 ± 6 %
(d) 1.36 ± 0 %

Answer 1

Answer:

A) 1.35 ± 1.48 %

Explanation:

Number of values = 4

Mean value = sum of all the observations / total number of observations

Thus,mean value = Sum / 4

= 1.34+1.38+1.32+1.36/4

= 5.4/4= 1.35

Absolute for each observation = ( Values - Mean Value)

Thus the values will be - 0.01, 0.03, 0.03, 0.01

Relative error = sum of absolute errors / number of observations

Relative error = 0.01+0.03+0.03+0.01/4

Here Relative error = 0.08 / 4 = 0.02

Percentage error = (Relative error × 100) / mean

=(0.02×100) / 1.35

= 2/1.35

= 1.48%

Thus, the mean value of refractive index with percentage error is 1.48%