Three parallel glass slabs of refractive indices 1.5, \(\sqrt{3}\) and 1.5 respectively have widths 2 mm, 1 mm and 4 mm. The combination is in air. Light is incident at the first slab at an angle of incidence \(\frac{\pi}{3}\). What is the angle with respect to the normal at which the light will emerge from the final surface?
\(\frac{\pi}{3}\)
For a set of parallel-faced slabs placed between the same medium (air) on both sides, Snell's law gives \(n_{0}\sin\theta_{0} = n_{1}\sin\theta_{1} = n_{2}\sin\theta_{2} = n_{3}\sin\theta_{3} = n_{0}\sin\theta_{f}\), since the initial and final medium is air (\(n_{0}=1\)), irrespective of the individual slab indices and thicknesses. Hence \(\sin\theta_{f} = \sin\theta_{0}\), so the emergent ray makes the same angle with the normal as the incident ray, i.e. \(\theta_{f} = \frac{\pi}{3}\). The correct option is (c).
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