Measurement of the Refractive Index of a Prism

First Method. - The spectrometer requires adjusting and the prism levelling on its stand, as before. The angle of the prism must be measured, as described. To obtain an accurate result, it is necessary that the light which falls on the face of the prism should be a parallel pencil. One method of obtaining this has already been given. The following, due to Professor Schuster, may often be more convenient, and is, moreover, more accurate. Let us suppose that the slit is illuminated with homogeneous light, a sodium flame, for example, and the prism so placed that the light passes through it, being deflected, of course, towards the thick part. Place the telescope so as to view the refracted image. Then it will be found that, on turning the prism round continuously in one direction, the image seen appears to move towards the direction of the incident light, and after turning through some distance the image begins to move back in the opposite direction and again comes into the centre of the field. There are thus, in general, for a given position of the telescope, two positions of the prism, for which the image can be brought into the centre of the field of the telescope. In one of these the angle of incidence is greater than that for minimum deviation, in the other less. Turn the prism into the first of these positions; in general the image will appear blurred and indistinct. Focus the telescope until it is clear. Then turn the prism into the second position. The image now seen will not be clear and in focus unless the collimator happens to be in adjustment Focus the collimator. Turn the prism back again into the first position and focus the telescope, then again to the second and focus the collimator.

After this has been done two or three times, the slit will be in focus without alteration in both positions of the prism, and when this is the case the rays which fall on the telescope are parallel; for since the slit remains in focus, its virtual image formed by the prism is at the same distance from the telescope in the two positions of the prism; that is to say, the distance between the prism and the virtual image of the slit is not altered by altering the angle of incidence, but this can only be the case when that distance is infinite - that is, when the rays are parallel on leaving the prism; and since the faces of the prism are plane, the .rays emerging from the collimator are parallel also. Thus both telescope and collimator may be brought into adjustment.

The simplest method of measuring the refractive index is to observe the angle of the prism and the minimum deviation. We have seen how to measure the former. For the latter, turn the telescope to view the light coming directly from the collimator. When the prism is in position, it of course intercepts the light, but it can generally be turned round so as to allow sufficient light for the purpose to pass on one side of it. Clamp the telescope and adjust with the tangent screw until the intersection of the cross-wires or the end of the needle comes exactly into the centre of the slit; then read the scale and vernier. Repeat the observation several times and take the mean of the readings. If it be impossible to turn the prism without removing it from its place, so as to view the direct image, a method to be described later on may be used.

Turn the prism to receive on one face the light emerging from the collimator, and move the telescope to view the refracted image.

Place the prism so that the deviation of the refracted light is a minimum. To determine this position accurately, turn the prism round the axis of the circle so that the refracted image appears to move towards the direction of the incident light, and continue the motion until the image appears to stop. This position can easily be found roughly. Bring the cross-wire of the telescope to cover the image of the slit, and again turn the prism slightly first one way and then the other. If for motion in both directions the image appears to move away from the direction of the incident light, the prism is in the required position. In general, however, for the one direction of rotation the motion of the image will be towards the direct light, and the prism must be turned until the image ceases to move in that direction. The first setting gave us an approximate position for the prism. By bringing the cross-wires over the image, and then moving the prism, we are able to detect with, great ease any small motion which we should not have noticed had there been no mark to which to refer it Having set the prism, place the telescope, using the clamp and tangent screw so that the cross-wire bisects the image of the slit, and read the vernier.

Displace the prism and telescope, set it again, and take a second reading. Repeat several times. The mean of the readings obtained will be the minimum deviation reading, and the difference between it and the mean of the direct readings the minimum deviation. With a good instrument and reasonable care the readings should not differ among themselves by more than 1'.

Having obtained the minimum deviation D, and the angle of the prism i, the refractive index μ is given by

To check the result, the prism should be turned so that the other face becomes the face of incidence, and the deviation measured in the opposite direction.

If we cannot observe the direct light, we may note the deviation reading on each side of it - that is, when first one face and then the other is made the face of incidence - the difference between the two readings is twice the minimum deviation required, while half their sum gives the direct reading.

To determine the refractive index of a liquid we must enclose it in a hollow prism, the faces of which are pieces of accurately worked plane parallel glass, and measure its refractive index in the same way as for a solid.

Experiment - Determine the refractive index of the given prism.

Enter results thus:

Second Method. - The following is another method of measuring the refractive index, which is useful if the angle of the prism be sufficiently small. Let the light from the collimator fall perpendicularly on the face of incidence. Then if i be the angle of the prism and D the deviation, since, using the ordinary notation,

and μ = sin ψ/sin ψ' = sin(D+i)/sin i.

We require to place the prism so that the face of incidence is at right angles to the incident light.

Turn the telescope to view the direct light and read the vernier.

Place the prism in position and level it, as already described. Turn the telescope so that the vernier reading differs by 90° from the direct reading. Thus, if the direct reading be 183° 15' 30", turn the telescope till the vernier reads 273° 15' 30". This can easily be done by the help of the clamp and tangent screw. Clamp the telescope in this position; the axes of the collimator and telescope are now at right angles.

Turn the prism until the image of the slit reflected from one face comes into the field, and adjust it until there is coincidence between this image and the cross-wire. The light falling on the prism is turned through a right angle by the reflexion. The angle of incidence is therefore 45° exactly. Read the vernier attached to the table on which the prism rests, and then turn the prism through 45° exactly, so as to decrease the angle of incidence; then the face of incidence will evidently be at right angles to the incident light Now turn the telescope to view the refracted image, and read the vernier; the difference between the reading and the direct reading is the deviatioa The angle of the prism can be measured by either of the methods already described; it must be less than sin^-1 (1/μ), which for glass is about 42°, otherwise the light will not emerge from the second face, but be totally reflected there. The refractive index can now be calculated from the formula.

A similar observation will give us the angle of incidence at which the light falls on any reflecting surface; thus turn the telescope to view the direct light, and let the vernier reading be α, then turn it to view the reflected image, and let the reading be β. Then α - β measures the deflection of the light, and if φbe the angle of incidence, we can show that the deviation is 180°-2φ.

Experiment. - Determine the refractive index of the given prism for sodium light.

Enter the results thus: