Refraction and Lenses Legacy Problem #4 Guided Solution
Problem*
A light ray is passing through water (n=1.33) towards the boundary with a transparent solid at an angle of 56.4°. The light refracts into the solid at an angle of refraction of 42.1°. Determine the index of refraction of the unknown solid.
Audio Guided Solution
Nature seems to follow very predictable laws, and one example of this is the refraction of light at a boundary, which seems to follow Snell's Law. Snell's Law is often stated as n1 times the sine of theta 1 equal n2 times the sine of theta 2. The n's represent indexes of refraction of the various mediums, medium 1 and medium 2. And the theta represents angles with respect to the normal line. So here we're told that light is traveling through water, and we're given the n value of the water. That would be n1, n1 equal 1.33. We're told that it approaches the boundary at an angle of 56.4 degrees. That's the angle in air, so that would be theta 1. It refracts into the solid at an angle of refraction of 42.1 degrees. That's theta 2, and what we wish to calculate is n2, the index of refraction of that unknown solid. To do that, I'm going to have to substitute my numerical values into the Snell's Law equation. It becomes 1.33 times the sine of 56.4 degrees is equal to n2 times the sine of 42.1 degrees. Now I have to divide each side by the sine of 42.1 degrees, and then evaluate the side with all the numbers in it. That would end up giving me an n2 value of 1.6524, and I can round that to three significant digits.
Solution
1.65
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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