Three flat layers of transparent material are stacked upon one another. the top layer has index of refraction n1, the middle has n2 and the bottom one has n3. if n1 > n2 > n3, and if a ray of light strikes the top layer at an angle of incidence , in which layer is the angle of refraction the greatest?

A light changing mediums from lower to the higher index of refraction will bend towards the normal (become more like perpendicular to the surface), i.e. the angle is going to decrease. 
So if x is the angle of incidence for the 1st layer, its angle of refraction is going to be y, and y<x. 
From the 1st layer light enters an even denser 2nd layer, so the ray bends even more toward the normal and the angle of refraction z<y. If there were a lot of layers, getting denser as you go down, the light would eventually be traveling almost vertically downwards. The largest angle of refraction is the top layer because of this.

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