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About the Measuring the Sugar Content with a Laser Project
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deleted-330307
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About the Measuring the Sugar Content with a Laser Project
In the procedure there was an equation given to find the index of refraction. Where was this equation found? Whats the number "2.00056" in the equation, and anything else that you may know about it would be helpful. The equation was "n = 2.00056 × sin[0.5(θmd + 60°)] ".
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deleted-330307
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Re: About the Measuring the Sugar Content with a Laser Project
Could someone also explain step 21. Why is the ratio of x/L the tangent of the angle of minimum deviation. And why did we use arctan to find the angle?
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norman40
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Re: About the Measuring the Sugar Content with a Laser Project
Hello Hunter626,
I’m assuming that you are working on the project described here:
https://www.sciencebuddies.org/science- ... ml#summary
The equation you referenced (equation 5 in the project background section) is a derivation from Snell’s Law. Starting with equation 1 shown in the background section and working through the two media changes (air/solution; solution/air) you end up with equation 2. After “plugging in” known numerical values you have equation 4. Simplifying equation 4 by dividing by 0.5 gives equation 5. The value of 2.00056 is 1.00028 (refractive index of air) divided by 0.5.
In the experimental set-up shown in the procedure section, distances x and L are two sides of a right triangle. The angle between these sides is the angle of minimum deviation. The hypotenuse of the triangle is made by the refracted laser beam.
The tangent of an angle is defined as the ratio of the length of the side opposite the angle (x in this case) to the length of the side adjacent to the angle (L). So the tangent of the angle of minimum deviation is x/L.
But you really want the angle, not the tangent of the angle. The arctangent function is the inverse of the tangent. So the arctangent of x/L gives the angle whose tangent is equal to x/L.
Some additional information about tangent and arctangent functions can be found at these links:
https://www.mathsisfun.com/sine-cosine-tangent.html
https://en.wikipedia.org/wiki/Inverse_t ... _functions
I hope this helps. Please post again if you have more questions.
A. Norman
I’m assuming that you are working on the project described here:
https://www.sciencebuddies.org/science- ... ml#summary
The equation you referenced (equation 5 in the project background section) is a derivation from Snell’s Law. Starting with equation 1 shown in the background section and working through the two media changes (air/solution; solution/air) you end up with equation 2. After “plugging in” known numerical values you have equation 4. Simplifying equation 4 by dividing by 0.5 gives equation 5. The value of 2.00056 is 1.00028 (refractive index of air) divided by 0.5.
In the experimental set-up shown in the procedure section, distances x and L are two sides of a right triangle. The angle between these sides is the angle of minimum deviation. The hypotenuse of the triangle is made by the refracted laser beam.
The tangent of an angle is defined as the ratio of the length of the side opposite the angle (x in this case) to the length of the side adjacent to the angle (L). So the tangent of the angle of minimum deviation is x/L.
But you really want the angle, not the tangent of the angle. The arctangent function is the inverse of the tangent. So the arctangent of x/L gives the angle whose tangent is equal to x/L.
Some additional information about tangent and arctangent functions can be found at these links:
https://www.mathsisfun.com/sine-cosine-tangent.html
https://en.wikipedia.org/wiki/Inverse_t ... _functions
I hope this helps. Please post again if you have more questions.
A. Norman