Refraction and Lenses Legacy Problem #15 Guided Solution
Problem*
In a physics lab, Jerome and Gavin are assigned the task of determining the critical angle of solid, transparent prism using laser light. When surrounded by air, light is observed to undergo total internal reflection when the angle of incidence is as low as 38°. Calculate the index of refraction of the material which the prism is made of.
Audio Guided Solution
In this question, two students, Shuram and Gavin, are given a prism, and they shine light into the prism, and they observe that once it gets into the prism and attempts to exit into the surrounding air, that at angles as low as 38 degrees, a total internal reflection occurs. That is, at angles of 38 degrees and higher, light stays within this transparent prism and fails to refract out. So we can regard this 38 degrees to be the critical angle, the angle of incidence upon the prism-air boundary that causes the angle of refraction to be 90 degrees. So what we'll do to solve for the index of refraction of the material is we'll use Snell's Law, and 38 degrees is the critical angle, or the angle of incidence, causing a 90 degree refracted angle. So we'll say N times the sine of 38 is equal to 1.00 for air, times the sine of 90 degrees. And then we'll make an effort to solve for N. We'll have to evaluate what the right side of the equation is, and that comes out to be perfectly 1. And then we'll divide 1 by the sine of 38 degrees. That will give us a value of 1.6243, and we can round that to the third significant digit.
Solution
1.62
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities and record them in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(\descriptive{d_o}{d_o,distance object} = 24.8\unit{cm}\); \(\descriptive{d_i}{d_i,distance image} = 16.7\unit{cm}\); \(\descriptive{f}{f,focal length} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
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