Angular dispersion through a prism? Rather

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The discussion focuses on calculating the angle of deviation for red light passing through a prism with an apex angle of 58.4 degrees and an incidence angle of 51.4 degrees, using the index of refraction values for violet and red light in silica flint glass. The user is struggling with the application of Snell's law and has derived an incorrect angle of deviation. Additionally, there is a related problem involving the exit angle of a light ray passing through a dense flint glass prism immersed in water, where the user seeks assistance due to time constraints. The forum emphasizes the importance of showing work for effective learning rather than simply providing answers. Overall, the discussion highlights challenges in optics calculations and the need for collaborative problem-solving.
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(a) The index of refraction for violet light in silica flint glass is 1.65, and that for red light is 1.61. What is the angle of deviation for the red ray passing through a prism of apex angle 58.4o if the angle of incidence is 51.4o? Units of o (degrees)

(b) What is the angular dispersion of visible light with the same angle of incidence? Units of o (degrees)




I am using n1sin(theata1)=n2sin(theata2) with no avail. I broke the equation into its 2 parts, but derived 4.275o (under the impression that angle of deviation=angle of dispersion), to no avail. I've got a 3rd problem which would also be great if someone could take a look, as I believe it is along similar lines to the above, which must mean that I'm making the same mistake on both:

A light ray is incident normally on one face at 25o-65-90o block of dense flint glass (prism) that immersed in water. Find the exit angle (theata4) on the light ray. n2=1.77, n1= 1.333.

I'm working on a relatively (very) brief time line, so any help would be greatly appreciated. Thanks in advance.
 
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I understand the urgency.But we at PF appreciate some work to be shown.
IF WE JUST TELL YA THE ANSWERS IT SHALL NEVER HELP YA IN THE LONG RUN.
 
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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