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Investigating the variation of refractive index with solute concentration - a possible approach NB. A Google search with the key words “variation refractive index solute concentration” throws up several useful sites. The approach outlined below derives from one of them. Consider a cell made out of glass as shown in the plan view. This could be made from microscope slides and a suitable adhesive. It is advantageous to keep the cell small. If a beam of light is allowed to pass through the cell it will emerge deviated because of the combination of the oblique partition and the differential refractive index. Consider the light ray ABCD in the second diagram. It is incident normally on the first glass face and passes into liquid 1 of refractive index n. In the analysis which follows, the parallel-sided glass pieces are ignored as (if they are indeed parallel-sided) they will have no effect on the final emergent angle . In the diagram: = the angle of the oblique partition = the angle of incidence on the liquid-liquid interface at B = the angle of refration at the liquid-liquid interface at B = the angle of emergence of the ray from the cell at C. By considering a triangle defined by the ray BC, the oblique glass partition and the right-hand end of the cell, it is straight-forward to show that the angle of incidence at C is - . Applying Snell’ Law at B and C respectively: n sin n n sin and n n sin 1sin (as the refractive index of the air = 1.00) If and n are small, then so will , - and be and , so we can apply the small-angle approximation to these equations which then become: n n n and n n The subtraction of one equation from the other and a small amount of manipulation leaves: n So a measurement of and a knowledge of allow n to be found. Practical details It is probably easiest to use a laser pointer as the light source (monochromatic and well-collimated) and determine by measuring the displacement of the light spot at the end of a long laboratory. e.g. for = 50 and n = 0.01, a 2.5 mm displacement is obtained from a 3 m light path. Clearly for n = 0.1 then the displacement would be 25 mm, which should be easily measurable. NB. Laser precautions. Gareth Kelly WJEC January 2003