Why Does the Calculator Show an Error When Solving for the Angle of Incidence?

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SUMMARY

The discussion focuses on the application of Snell's Law to determine the angle of incidence when a light beam exits water at an angle of 68° to the vertical. The correct formulation of Snell's Law is highlighted as n1sin(θ1) = n2sin(θ2), where n1 is 1.33 (the refractive index of water), n2 is 1 (the refractive index of air), and θ2 is 68°. The error encountered on the calculator arises from an incorrect setup of the equation, which is clarified by the participants in the discussion.

PREREQUISITES
  • Understanding of Snell's Law in optics
  • Knowledge of refractive indices (n1 and n2)
  • Basic trigonometric functions, specifically inverse sine
  • Familiarity with calculator functions for trigonometric calculations
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  • Study the derivation and applications of Snell's Law in optics
  • Learn how to calculate angles of incidence and refraction using different mediums
  • Explore common errors in trigonometric calculations on scientific calculators
  • Investigate the impact of refractive indices on light behavior at interfaces
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Students in physics, educators teaching optics, and anyone interested in understanding light behavior at water-air interfaces.

mustang1988
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b]1. A light beam coming from an underwater spotlight exits the water at an angle of 68° to the vertical. At what angle of incidence did it hit the air-water interface from below the surface?


2. snell's law n1sin\Theta1=n2sin\Theta2



3. sin\Theta1=1.33(sin68)
After doing this I took the inverse sin of it and it comes up as error on my calculator. I know it should be an easy question but I don't know where I am messing up.
 
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It looks like you've got the equation set up wrong. It should read:

n_1\sin{(\theta_1)} = n_2\sin{(\theta_2)}

Where n_1 = 1.33, n_2 = 1, and \theta_2 = 68.
 
I knew it would be something dumb, thanks for your help.
 

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