A cubical block is made from two equal-size slabs of materials with different re

Question

A cubical block is made from two equal-size slabs of materials with different refractive indices, as shown in the figure below. A ray of light is incident on the mid point of the first slab at an angle of 35degree. (a) Construct the refracted ray through this first half of the cube, using a protractor, (b) Find the index of refraction of the right-hand slab, (c) Continue your ray tracing through the cube and out into air again using the newly gained information about the index of refraction, (d) What time does it take light to travel through the cube? The length of the side of the cube is 20cm.

Explanation / Answer

let angle of refracted ray in first slab be theta sin(35)/sin(theta) = 1.43 theta = 23.64 degrees let width of slab be w tan(theta) = y / w = 0.437 and new location of the incoming light = 10 + y from the top = 10 - y from the bottom now let new angle of refraction be phi sin(phi)/sin(theta) = 1.43/n and tan(phi) = [10 - y]/w = [10 - 0.437w]/w phi = arctan([10 - 0.437w]/w) n = 0.573/sin(arctan([10 - 0.437w]/w)) but w = 5cm n = 0.573/sin(arctan([10 - 0.437*5]/5)) = 1.36

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