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Explanation:
Step 1: Description of the Usual Method for Determining the Refractive Index of a Rectangular Glass Slab Using a Protractor.
Once the outline of the rectangular glass slab is drawn on the piece of paper (thin lines in the above diagram) and the pins removed, the following steps are carried out (refer to the above diagram):
two straight lines (AB and CD) are drawn with each line passing through one of the pairs of pin holes made by the pins and extended to the surface of the glass slab nearest the position of the two holes; these lines do not extend inside the glass slab; they represent the incident (AB) and emergent (CD) rays;straight lines (EF and GH) are drawn normal to the surfaces of the glass slab that pass through the point where the lines drawn in the previous step intersect the surfaces of the glass slab; these lines are drawn so that they lie outside and inside the glass slab;a straight line (BC) is drawn between each of the points of intersection made by the normal lines drawn in the previous step and the surfaces of the glass slab; this line represents the refracted ray;measure the angle of incidence (angle ABE) which is the angle between the incident ray and the normal that the incident ray makes with the glass surface;measure the angle of refraction (angle CBF or angle BCH) which is the angle between the refracted ray and either of the normals that the incident ray or the emergent ray makes with the glass surface;measure the angle of emergence (angle DCG) which is the angle between the emergent ray and the normal that the emergent ray makes with the glass surface; while this sub-step is not necessary for computing the RI, it is measured to show that the angle of incidence is equal to the angle of emergence and thus that the incident and emergent rays are parallel.
Following these measurements, the refractive index (RI) of the glass is obtained by taking the ratio of the sine of the angle of incidence to that of the sine of the angle of refraction.
This procedure is then repeated for a number of different incident angles to show that the ratio of the sine of the angle of incidence to that of the sine of the angle of refraction should remain constant when a number of different values are used for the incident angle.
Step 2: Description of a Procedure for Finding the Sines of the Angles Made by the Incident and Refracted Rays Without Using a Protractor.
In this procedure it is not necessary to trace the complete outline of the glass slab; only the opposite surfaces through which the light rays travel need be indicated as shown in the above diagram, where the thin lines represent these two surfaces.
The three initial sub-steps of Step 1 are carried out except that Sub-step 1 is modified by extending the lines AB and CD (broken lines) as follows:
extend the incident ray AB forwards so that it cuts the opposite face of the glass slab at point I; this is the path that the incident ray would follow if the glass slab were absent;extend the emergent ray CD backwards so that it cuts the opposite face of the glass slab at point J.
If the incident and refracted rays when extended do not cut the surfaces of the glass slab at points I and J extend the lengths representing these surfaces so that points I and J can be found.
BHCF is a rectangle formed by the surfaces of the glass slab and the normals to the surfaces at points B and C; its diagonal BC represents the path followed by the refracted ray through the glass slab.
From the geometry of the various right-angled triangles in the above diagram, note:
the angle of incidence, angle ABE, is equal to the angle FBI and its sine is equal to the ratio of lengths FI over BI;the angle of emergence, angle DCG, is equal to the angle HCJ and its sine is equal to the ratio of lengths HJ over CJ;the angle of refraction is angle CBF (or angle BCH) and its sine is equal to the ratio of lengths FC over BC (or the ratio of lengths BH over BC).
Thus, without using a protractor or having to work out the sines of angles using a calculator with trigonometric functions (or trigonometric tables), the sines of the various angles needed for calculating the RI of the glass slab can be simply found from measurements of various length.
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