This is NOT about calculating the minimum deviation of a prism. You are given only two pieces of information: the angle of the prism, the refractive index of the medium (glass), and you know that the input ray is horizontal (parallel to the base of the prism). The refractive index of the entry material is air, so refractive index is unity. Is it possible to derive the deviation of the beam in terms of prism angle without knowing the exact angle of incidence? I have been on a whiteboard scratching my head trying to derive this one...
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1$\begingroup$ If you know the angle of the prism, and that the incident ray is parallel to the base, that tells you the angle of incidence. It's just geometry. $\endgroup$– RogerJBarlowCommented May 27, 2021 at 16:51
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$\begingroup$ @RogerJBarlow - The angle of incidence is measured normal to the material, so I am unsure how you could go from prism angle -> incidence $\endgroup$– Ryanator13Commented May 27, 2021 at 16:55
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$\begingroup$ Is the prism cross-section at least an isosceles triangle? $\endgroup$– DJohnMCommented May 27, 2021 at 17:14
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$\begingroup$ @DJohnM No - consider it unknown $\endgroup$– Ryanator13Commented May 27, 2021 at 20:08
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$\begingroup$ This kind of optical prisms are always isosceles. If its not, there is not enough information for this problem. $\endgroup$– José AndradeCommented May 27, 2021 at 22:33
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2 Answers
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Draw the perpendicular. The angles shown as $a$ are all equal
answered May 27, 2021 at 17:19
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$\begingroup$ did you draw the diagram? if yes, what website or app did you use pls? $\endgroup$ Commented May 27, 2021 at 17:26
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$\begingroup$ Thank you for drawing this out - been a minute since I have done trig, and another set of eyes always helps, so I appreciate it! $\endgroup$ Commented May 27, 2021 at 18:08
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$\begingroup$ @ChristinaMelita I drew it using R. $\endgroup$ Commented May 27, 2021 at 18:37
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$\begingroup$ Does this assume that the prism equilateral or isosceles? Because if it were scalene, it is not necessarily true that the normal line bisects the triangle. $\endgroup$ Commented May 27, 2021 at 19:58
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Hints: Line AB is straight, EDC is 90 degrees, CDB can be found in terms of $\theta$, so ADE can be got in terms of $\theta$ and that's the angle of incidence you need.
answered May 27, 2021 at 18:13
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$\begingroup$ This leaves CBD as an unknown - it is not for certain an isosceles triangle $\endgroup$ Commented May 27, 2021 at 20:09
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$\begingroup$ Either the question you were given has different answers depending on CBD (in that case it's impossible to do) or the same answer as CBD varies - and in that case you can assume it's an isosceles triangle and get the answer. $\endgroup$ Commented May 27, 2021 at 21:50