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'O' Level Standard Questions - Refraction

Q8. A prism made of glass with a refractive index of 1.50 has two angles of 75° and one of 30°.

Determine whether a ray of light be reflected and/or refracted at one of the longer sides if it enters the prism normally onto

(a) the other longer side,

(b) the shorter side.

To determine whether total internal reflection will occur we need to determine the critical angle of the glass.

Snell's Law: n1sin θ1 = n2sin θ2

nairsin θair = nglasssin θglass

sin 90o = 1.50 x sincritical for glass

sincritical for glass = sin 90o/1.5 = 1/1.5 = 0.666

Critical angle for glass = 41.8o

See the notes on total internal reflection for more information.

30o is less than the critical angle so the ray will not suffer total internal reflection. Some of the light will be refracted - and some reflected.

nairsin θair = nglasssin θglass

sin θair = 1.50 x sin 30o

sin θair= 0.75

θair= 49o

(a) The ray therefore leaves the glass. However some of the light will be reflected back into the prism

- this is shown as fainter traces in the graphic.

For part b we only need to use a little geometry to see that the angle of incidence on the side of the glass is 75o. This is larger than 42o - the critical angle - therefore total internal reflection will occur and no refraction only reflection will take place.