A technician performs an experiment on a glass slap and finds that the critical angle for total internal reflection at the glass (refractive index n1) air (refractive index n2 = 1) interface is 43 +/- 2 deg. Find n1 and the associated error.
Slap or slab?
Solve
n1*sin43 = n2 sin90
n1 = 1/sin43
For the associated error, use the same formula with angles of 41 and 45 degrees.
questions
To find n1 and the associated error, we can use the relationship between the critical angle, n1, and n2.
The critical angle (θc) for total internal reflection can be calculated using the formula:
θc = arcsin(n2/n1)
Rearranging the formula, we have:
n1 = n2 / sin(θc)
Given that n2 = 1 (since it refers to air), we can substitute it into the equation:
n1 = 1 / sin(θc)
Now, we need to consider the error in the critical angle. Since the critical angle is given as 43 +/- 2 degrees, the minimum angle is 41 degrees (43 - 2) and the maximum angle is 45 degrees (43 + 2).
We can calculate the minimum and maximum values for n1 using these angles:
n1(min) = 1 / sin(θc(min))
n1(max) = 1 / sin(θc(max))
Substituting the respective angles into the formulas, we can find the values:
n1(min) = 1 / sin(41 degrees)
n1(max) = 1 / sin(45 degrees)
Using a scientific calculator, we can calculate these values:
n1(min) ≈ 1.4996
n1(max) ≈ 1.7321
Therefore, the refractive index n1 is approximately between 1.4996 and 1.7321.
To calculate the associated error, we can use the formula:
Error = (n1(max) - n1(min)) / 2
Error = (1.7321 - 1.4996) / 2
Error ≈ 0.11625
Therefore, the associated error is approximately 0.11625.