Move point B to change the apex angle of the prism.
Move point E to change the angle of incidence.
Move point D as needed to control where light strikes the right side of the prism.
Use sliders to change the indices of refraction of the prism and what the prism is surrounded by.

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What happens when the indices of refraction are identical?
What does it mean when the outgoing ray disappears?
For a given prism, what can you change to make the ray disappear?
For a given angle of incidence and apex angle, can you make the ray disappear?

Lenore Horner, Created with GeoGebra