Measuring the Index of Refraction

A laser produces a thin, collimated beam of coherent light. If that beam passes through a glass plate with parallel faces, the exiting beam is parallel to the incident beam; however, it will be displaced if the faces are not perpendicular to the incident beam. We can measure the index of refraction of glass by measuring the dependence of that offset on the incident angle.

We will use an optical bench, a laser, a glass plate, a linear translator, a photometer with a probe, an angular translator and a micrometer.

Name:

Lab Partners:

When entering numeric data, use exponentials: ie., 1.6 * 10-19 = 1.6E-19.

Procedure

  1. Measure the thickness t of the glass plate with the micrometer:
    t = mm

  2. Set up the optical bench as follows:

    Adjust the glass plate until it is perpendicular to the bench. Adjust the photometer to its least sensitive setting. Find the position of the beam by locating the maximum photometer value. Record the knob setting on the linear translator:

    k0 =

  3. Rotate the plate 15 degrees counterclockwise and note the knob position corresponding to the maximum beam intensity. Note that you must add 10 each time you rotate the knob past zero.
    k15 =

  4. Repeat step 3 for 30 and 45 degrees, working quickly. The photometer loses sensitivity in time:
    k30 = k45 =

Analysis

  1. Each number on the knob represents .1 mm. Compute the beam displacements using the formula
    dq = (kq - k0) / 10

    d15 = mm d45 = mm
    d30 = mm

  2. Consider the following diagram:

    Using

    tan q' = x / t,
    tan q = (x + y) / t and
    cos q = d / y,
    where d is the positive distance from the first maximum, we find that
    d / t = cos q (tan q - tan q'),
    which allows us to compute
    q' = tan-1 ((sin q - d / t) / cos q)
    Calculate q' for each angle q (= 15, 30 and 45 degrees):
    q '15 = degrees q '45 = degrees
    q '30 = degrees

  3. Assuming that the index of refraction of air is 1, use Snell's Law
    n1 sin q1 = n2 sin q2
    to calculate
    n = sin q / sin q'
    for each angle:
    n15 = n45 =
    n30 =
    Calculate the average and the absolute uncertainty in this quantity:
    navg = Dn =
    Compare with the range quoted for the index of refraction of glass in your text:

©2005, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

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