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I am reviewing some concepts on light and came across a question that puzzled me. A beam of light is incident from a glass into air. The incident ray is 60 degrees to the normal. The question actually provides an image of this scenario with multiple possible refracted rays and asks to select the correct one. The correct answer is a refracted ray that is pushed farther away from the normal. While qualitatively this makes sense (the light is going to a less dense material), I am confused as to how quantitatively this works out:

Using Snell's Law: 1.5 * sin( 60 ) = 1 * sin ( theta ), with theta being the angle between the normal and the refracted ray. But 1.5 * sin ( 60 ) = 1.299, which makes finding theta impossible? So what does this mean about the refracted ray?

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It's a poorly written question. As you have discovered, a ray incident on the glass side of the interface at 60° to the normal would be totally internally reflected and there would be no transmitted ray. Well, not unless it's glass with an unusually low refractive index.

It's possible there is a misprint and they mean the angle is 60° to the surface i.e. 30° to the normal.

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Using Snell's law when light travels from glass to air,

$$ 1.5\sin(i) = sin(r)$$

If $\sin(i)=2/3$ then the refracted ray grazes the surface as $r=90^o$. If the value of $i$ is greater than this value, total internal reflection (TIR) takes place.

For any $i$ greater than around $42^o$ in glass to air interface TIR would take place.

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