Refraction and Lenses Legacy Problem #5 Guided Solution
Problem*
During a physics lab, Ray Zuvlight observes a laser line passing through an unknown material towards a boundary with air with an angle of incidence of 24.5°. The light ray emerges into the air with an angle of refraction of 33.8°. Determine the index of refraction of the unknown material.
Audio Guided Solution
Nature seems to follow very predictable laws. One example of such laws is the refraction of light at a boundary, which seems to follow Snell's Law. Snell's Law can be stated mathematically as n1 times the sine of theta 1 equals n2 times the sine of theta 2. Hearing this question, we are told that laser light is moving through an unknown material and approaches the boundary with air. Within the unknown material, the angle of incidence is 24.5 degrees. Once it goes into air, it refracts at 33.8 degrees. So what we know are three bits of information. That is, if we know that the index of refraction of air is 1.00. So what we can say is that the n1 is the unknown and the theta 1 is the 24.5 degrees. We will call it medium 1, the unknown material. And then for medium 2, we call that the air and its n2 value is 1.00. And its theta 2 value is 33.8 degrees. So I set up Snell's Law like this. n1 times the sine of 24.5 degrees is equal to 1.00 times the sine of 33.8 degrees. And then I make an effort to solve for n1. I begin by dividing both sides of the equation by 24.5 degrees. It shows up on the right side with the n2 and the theta 2 values. And then I evaluate the right side of the equation. And that gives me the value of n1. It comes out to be 1.3415. And I can round that to three significant digits.
Solution
1.34
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.
Read About It!
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