Investigating Total Internal Reflection

The critical angle of a material, and so its refractive index, can be measured using a semicircular glass block and a ray box.Method:
1. Place the block on white paper, flat face away from the ray box, and draw round it. Mark the centre of the flat face.
2. Aim a narrow ray at the curved face so that it travels along a radius towards the centre of the flat face. Because it meets the curved surface along the normal, it enters without being refracted.
3. At the flat face the ray passes from glass to air. Move the ray box round, keeping the ray aimed at the centre, to increase the angle of incidence.
4. Stop when the refracted ray just travels along the flat face (the boundary). Mark the incident ray and measure the angle between it and the normal. This is the critical angle C.Beyond this angle the light is totally internally reflected, and you can check the reflected ray obeys the law of reflection.Analysis: for glass to air, n = 1 / sin C.Worked example: a student measures C = 42°. n = 1 / sin 42° = 1 / 0.669 = 1.49.Improving results: the change from a faint grazing ray to total reflection is gradual, so approach the critical angle from both sides and take the mean. Repeat the measurement several times to reduce the effect of random errors. Use a darkened room and the narrowest possible ray.