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

AI Thread Summary
The discussion revolves around calculating the angle of incidence for a light beam exiting water at an angle of 68° to the vertical. The correct application of Snell's Law is emphasized, with the equation n1sin(θ1) = n2sin(θ2) being crucial. The user initially misapplied the formula, leading to an error on their calculator when attempting to find the angle of incidence. The correct values are n1 = 1.33 for water, n2 = 1 for air, and θ2 = 68°. Clarifying the setup of the equation resolved the confusion and highlighted the importance of proper formula arrangement.
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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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