Refraction Problem Set: Question 8 Dr. John Lloyd University of Toronto
Question 88. A horizontal light ray strikes a right angled polycarbonate prism (n = 1.66), positioned with its shortest side parallel to the floor. The superior apex of the prism has a 30° angle. a) What is the prism power? b) Will the prism power be more or less if the triangle is tilted slightly away from the light ray?
Answer 88. A horizontal light ray strikes a right angled polycarbonate prism (n = 1.66), positioned with its shortest side parallel to the floor. The superior apex of the prism has a 30° angle. a) What is the prism power? 49 prism diopters b) Will the prism power be more or less if the Less triangle is tilted slightly away from the light ray?
Answer 8Prism Power describes the amount of deviation produced as light passes through aprism, and is measured in Prism Diopters (Δ or PD)By convention, 1 Prism Diopter is defined as a deviation of 1 cm at a distance of 1 mIn this case, we can use the principles of refractionto determine how much the light will be deviated 30°by the given prism
Answer 8 Calculate the angle of incidence (φi):30° 90° Along a straight line (the normal in this case), the 60° total of all angles must add to 180°φi φi + 60° + 90° = 180° φi = 30°
Answer 830° Use Snell’s Law to calculate the angle of transmission (φt) 60° φtφi ni sin φi = nt sin φt 1.66 sin 30°= 1 sin φt φt= 56.10° n = 1.66 n=1
Answer 8 We need to calculate the angle at which the light deviates from the horizontal plane (φ2) Using similar triangles, φ1 φt φ1 = φi= 30°30° φ2 Then, it can be seen that: φt = φ1 + φ2 φ2 = 56.10° – 30° φ2 = 26.10°
Answer 8 Now we use trigonometry to calculate the deviation at a distance of 1 m tan 26.1° = opposite/adjacent 1m =x/126.1° x x = 0.490 m = 49 cm Therefore, the prism deviates the light by 49 cm at a distance of 1 m a) Prism Power, Δ = 49 PD
Answer 8b) The prism power was calculated for the Prentice Position, in which the front surface is perpendicular to the incident light such that all refraction occurs at the second surface Tilting the lens away from the light ray would shift the position toward the “Position of Minimum Deviation” in which there is equal bending at both surfaces of the lens As its name implies, there is less deviation in this position, and therefore, tilting the lens would DECREASE the prism power