The prism is made from glass and its cross section is an

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The discussion centers on calculating the angles of refraction for red and violet light as they exit a glass prism with an equilateral triangle cross-section. The indices of refraction for red and violet light are given as 1.662 and 1.698, respectively, with an angle of incidence of 60 degrees. Participants emphasize the need to apply Snell's Law, n1*sin(theta1) = n2*sin(theta2), but also highlight the importance of incorporating geometry to find the correct angles. The process involves calculating an intermediate angle and then using it to determine the emergence angle for both colors separately. Accurate application of these principles is crucial for obtaining the correct results.
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Homework Statement


the prism is made from glass, and its cross section is an equilateral triangle. the indices of refraction for the red and violet light are 1.662 and 1.698, respectively. the angle of incidence for both the red and violet light is 60 degrees. find the angles of refraction at which the red and violet rays emerge into the air from the prism

Homework Equations


I know I'm supposed to use the formula n1*sin theta 1=n2 *sin theta 2.

The Attempt at a Solution



I tried plugging in 60 degrees into theta 1, and i tried plugging n1 and n2 with the indices of refractions that are given. then using all those knowns i tried to solve for the unknown, theta 2, but it didn't give me the right answer. my answer was close, but it's not correct.
 
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you have to do a bit of geometry here first. see the attachment. U can find r by the formula u stated. Then use sin(60-r)/sin(x)=1/n to find the angle x at which they emerge. You have to do separately for the red and violet but using the same process
 

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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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