A plane mirror is used to trace out an incident beam and a reflected beam. The a

Question

A plane mirror is used to trace out an incident beam and a reflected beam. The angle of incidence is measured to be (12.5plusminus 0.5)degree and the angle of reflection is measured to be (13.0 plusminus 0.5)degree Do these agree within uncertainty? A ray is incident upon a Plexiglas block. The angle of incidence is (22.0 plusminus 1.0) degree. The refracted ray is measured to be (15.0plusminus 1.0)degree. A) Use Snell's law to calculate the index of refraction for the Plexiglas (including uncertainty). B) Compare n, as calculated in part A) with the accepted value of n for Plexiglas of 1.5.

Explanation / Answer

1. Yes. By law of reflection, the incidence angle = the reflection angle. The incidence angle is between 12° to 13° and the reflection angle is between 12.5° to 13.5°. So the true values for both of them is between 12.5° to 13°

2. (a)  Snell's law states that ni sin(i) = nr sin(r)

nr = sin(i)/sin(r) = sin(22°)/sin(15°) = 1.4473

nr = (partial derivative of nr wrt i) i + (partial derivative of nr wrt r) r

nr = (cos(i)/sin(r)) i - (sin(i)/sin2(r))*cos(r) r

nr = 3.5823i - 5.4016r ( i and r should be in radians)

nr = +- 0.1568

(b) nr = 1.4473 +- 0.1568

The accepted value of 1.5 is covered in the calculated value.

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