Refer to Exercise 8. Assume the critical angle is measured to be 0.90 ± 0.01 rad. Estimate the refractive index and find the relative uncertainty the estimate.

Exercise 8: The refractive index n of a piece of glass is related to the critical angle by n = 1/sin. Assume that the critical angle is measured to be 0.700.02 rad. Estimate the refractive index, and find the uncertainty in the estimate.

Solution:

Step 1 of 1:

Given the refractive index n of a piece of glass is related to the critical angle by

.

We assume that the critical angle is measured to be rad.

Now we have to estimate refractive index and the uncertainty in the estimate.

Our goal is:

We need to estimate refractive index and the uncertainty in the estimate.

Now we have to find the estimate the refractive index.

Let the refractive index n of a piece of glass is related to the critical angle is

Here .

Then, the uncertainty in the estimate is

We are differentiating with respect to .

Then we know that .

Therefore the uncertainty in the estimate is 1.0259.