How Do You Calculate Light Refraction Angles Through Quartz?

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To calculate light refraction angles through quartz, Snell's Law is applied, using the refractive index of air (n1 = 1) and quartz (n2 = 1.458). The user encountered a calculator error while attempting to solve for the angle of refraction using the equation 1*sin(27) = 1.458*sin(x). Guidance was provided to ensure the calculator is set to degree mode to avoid confusion with the output. The discussion emphasizes the importance of correctly inputting values and settings in the calculator for accurate results. Understanding these principles is crucial for tracing light through different media.
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(SOLVED) Calculator Entry ErrorAngles of Reflection of Light

A ray of light strikes a flat 2.00 cm thick block of fused quartz (n = 1.458) at an angle of θ = 27.0° with the normal (Fig. P22.18). Trace the light beam through the fused quartz and find the angles of incidence and refraction at each surface.



Snell's Law=n1sintheta1=n2sintheta2



Since the ray of light began in air, I used 1*sin(27)=1.458*sin(x) and solved but my TI-89 gave me 360*@n6+.449605 which makes no sense to me. Could I get some guidance please?
I have to find the angles as it enters and leaves the quartz
 
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is your calculator in degree mode?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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