Angular dispersion through a prism? Rather

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SUMMARY

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 angle of incidence of 51.4 degrees, using the index of refraction values of 1.65 for violet light and 1.61 for red light. The user attempted to apply Snell's Law (n1sin(theta1) = n2sin(theta2)) but encountered difficulties, deriving an incorrect angle of deviation of 4.275 degrees. Additionally, the user seeks assistance with a related problem involving a light ray incident on a dense flint glass prism immersed in water, with refractive indices of n1=1.333 and n2=1.77.

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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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