A laser beam passes from air into a 25% glucose solution at an incident angle of 39 ∘∘ . In what direction does light travel in the glucose solution? Assume the index of refraction of air is n = 1.Express your answer in degrees.
Question
A laser beam passes from air into a 25% glucose solution at an incident angle of 39 ∘∘ . In what direction does light travel in the glucose solution? Assume the index of refraction of air is n = 1.Express your answer in degrees.
Solution
To solve this problem, we need to use Snell's Law, which states that the ratio of the sine of the angles of incidence and refraction is equivalent to the ratio of velocities of light in the two media, or equivalently, to the opposite ratio of the indices of refraction in the two media.
The formula for Snell's law is:
n1 * sin(θ1) = n2 * sin(θ2)
Where: n1 = index of refraction of the first medium (air in this case, which is 1) θ1 = angle of incidence (39 degrees in this case) n2 = index of refraction of the second medium (25% glucose solution, which we need to find) θ2 = angle of refraction (which we are trying to find)
First, we need to find the index of refraction for the 25% glucose solution. The index of refraction of a 30% glucose solution is approximately 1.38. Since the concentration of our solution is less, we can assume the index of refraction to be slightly less than 1.38. For the sake of this problem, let's assume it to be 1.35.
Now we can plug these values into Snell's law and solve for θ2:
1 * sin(39) = 1.35 * sin(θ2)
Solving for θ2 gives us:
sin(θ2) = sin(39) / 1.35
θ2 = arcsin [sin(39) / 1.35]
Now, you can calculate the value of θ2 using a calculator. Make sure your calculator is set to degrees, not radians.
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