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'O' Level Standard Questions - Refraction

Q7.

(a) Taking the refractive index of water as 1.33, what is the critical angle for water?

(b) The critical angle of diamond is 24°. What is its refractive index?

The critical angle is the angle of incidence upon a dense/rare boundary that produces and angle of refraction of 90o. Therefore you must ensure your 90o angle is applied to the denser of the two media!

Snell's Law: n1sin θ1 = n2sin θ2

nairsin θair = nwatersin θwater

sin 90o = 1.33 x sin θwater

sin θwater = 1/1.33 = 0.75

θc = 48.6o

(a) The critical angle for water is 48.6o

Snell's Law: n1sin θ1 = n2sin θ2

nairsin θair = ndiamondsin θdiamond

sin 90o = ndiamond x sin 24o

ndiamond = 1/sin 24o

(b) ndiamond = 2.46