find the %error in the measurement of refractive index of glass. the values was 1.54,1.53,1.44,1.54,1.56& 1.45.
To find the percentage error in the measurement of the refractive index of glass, you need to follow these steps:
Step 1: Calculate the average value of the measurements.
To do this, add up all the values for the refractive index and divide by the total number of measurements. In this case, there are 6 measurements:
1.54 + 1.53 + 1.44 + 1.54 + 1.56 + 1.45 = 8.06
Average refractive index = 8.06 / 6 = 1.3433 (rounded to four decimal places).
Step 2: Calculate the absolute difference between each measurement and the average.
To do this, subtract the average value from each individual measurement:
|1.54 - 1.3433| = 0.1967
|1.53 - 1.3433| = 0.1867
|1.44 - 1.3433| = 0.0967
|1.54 - 1.3433| = 0.1967
|1.56 - 1.3433| = 0.2167
|1.45 - 1.3433| = 0.1067
Step 3: Calculate the average absolute difference.
To find the average absolute difference, you add up all the absolute differences you calculated in step 2 and divide by the total number of measurements:
(0.1967 + 0.1867 + 0.0967 + 0.1967 + 0.2167 + 0.1067) / 6 = 0.1503
Step 4: Calculate the percentage error.
To find the percentage error, you divide the average absolute difference by the average refractive index and multiply by 100:
(0.1503 / 1.3433) * 100 ≈ 11.19%
Therefore, the percentage error in the measurement of the refractive index of glass is approximately 11.19%.