A diagram shows a ray of light travelling through three different transparent media having refractive indices μ1, μ2 and μ3 as shown. Points Q and R are points on the surfaces separating the media. Given PQ || RS.
(a) Among the three media shown, in which medium is the speed of light minimum?
(b) As the ray of light travels from medium 1 to medium 2, how does the wavelength of light change? (State whether it increases, decreases, or remains constant.)
(c) State the relationship between the refractive indices μ1 and μ3 that ensures the emergent ray (RS) is parallel to the incident ray (PQ).
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(a) When the light ray travels from Medium 1 to Medium 2, it bends towards the normal, indicating that Medium 2 is optically denser than Medium 1. When it travels from Medium 2 to Medium 3, it bends away from the normal, indicating Medium 2 is also denser than Medium 3. Because light travels slowest in the optically densest medium, its speed is minimum in Medium 2.
(b) The frequency of light does not change on refraction, and speed = frequency × wavelength. Since the speed of light decreases on entering medium 2, the wavelength also decreases.
Hence, the wavelength decreases.
(c) The emergent ray RS is parallel to the incident ray PQ only when the ray suffers equal and opposite bending at the two surfaces, i.e., when the first and the third media are optically identical.
Hence, μ1 = μ3.