The critical angle for a special glass in air is 41.0 degrees. What is the critical angle if the glass is...?

Question

The critical angle for a special glass in air is 41.0 degrees. What is the critical angle if the glass is immersed in water?

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I don't understand it.

Answer 1

The critical angle is the angle (measured from normal, or perpendicular, to the surface) at which total internal reflection (TIR) begins. TIR can occur when light passes from one medium into a less dense one. Light at 0° (normal to the surface) passes straight through, but light striking the surface at an angle is deflected by an amount that depends on the relative indices of refraction of the two media. You can see this in action if you go underwater and look up at the sky - you'll see a bright circle of sky straight above, but beyond the critical angle the surface of the water acts like a mirror.

You calculate this effect using Snell's law - n1·sinΘ1 = n2·sinΘ2, where the n's are the refractive indices and the Θs are the incident angles. At sinΘ2 = 1, the ray emerges parallel to the surface, which is to say, it doesn't emerge; Θ1 in this case is called the critical angle. So to find the critical angle, you set sinΘ2 = 1 and solve for Θ1;:
Θcrit = asin(n2/n1).

Assuming n(air) = 1 (it's not quite, but close enough), n(glass) = 1/sin(41°) = 1.524. n(water) = 1.33. So your glass-water critical angle is asin(1.33/1.524) = 60.8°.