A light ray strikes a 2 cm thick plate ( = 2.0 ) at an angle of 45^ relative to the normal. Determine the shift in the path of the light as it emerges from the plate.

Step-by-step solution

Using Snell's law at the first interface: i = r 45^ = 2.0 r 1 2 = 2 r r = 1 2 2 From this, we find r : r = 1 - ^2 r = 1 - 1 8 = 7 2 2 The lateral shift x of the emergent ray is given by: x = t (i - r) r = t ( i - i r) Substituting the values: x = 2 ( 45^ - 45^ r r ) x = 2 ( 1 2 - 1 2 1 / (2 2 ) 7 / (2 2 ) ) x = 2 ( 1 2 - 1 2 1 7 ) x = 1 - 1 7 Using 7 2.645 : x = 1 - 1 2.645 1 - 0.378 = 0.622 cm