Question

Snell's Law and the Law of Reflection explain how light is redirected when it encounters a surface between two media. In the extreme, light may only reflect at a boundary, and go back into the medium it was in. More often, some of it reflects and some goes through. If the boundary is plane and flat, then these laws are easy to interpret. When the boundary is curved, they describe happens at every point on the surface.

One of the classic types of glass is called "crown" glass, which has an index of refraction for visible light of 1.52 and is usually free of significant impurities. It was one of the first glasses discovered, and windows are made from it. Another glass is called "flint" glass, and it has lead oxide added, which makes it heavier, more "dispersive", and increases its index of refraction to 1.62.

1. A ray of light enters a flat surface of crown glass at a 25 degree angle to the surface. At what angles do the reflected and refracted rays leave the surface?

2. As in the first part, but for flint glass, what are the angles?

3. For the flint glass, the refracted ray goes through the glass to the other side. If the glass is a parallel slab, what happens when the ray reaches the opposite side from the inside? At what angle to the surface does it exit the glass back into air?

4. What is the smallest angle to the surface that light can have and still be transmitted from the inside to the outside in the case of flint glass? What angle is the light going at as it leaves in that case?

Hint: The laws of reflection and refraction are usually stated in terms of the angles to the perpendicular or "normal" to the surface. These questions are rephrased in terms of the angles to the surface so take care in interpreting the laws and your answers.

Answer 1

1.

For crown glass :

n_air = index of refraction of air = 1

n_crown = index of refraction of crown glass = 1.52

= Angle of incidence = 25 deg

= Angle of refraction = ?

Using snell's law

n_air Sin = n_crown Sin

1 Sin25 = (1.52) Sin

= 16.14 deg

= Angle of reflection = ?

Using law of reflection

=

= 25 deg

2)

For flint glass :

n_air = index of refraction of air = 1

n_flint = index of refraction of flint glass = 1.62

= Angle of incidence = 25 deg

= Angle of refraction = ?

Using snell's law

n_air Sin = n_crown Sin

1 Sin25 = (1.62) Sin

= 15.12 deg

= Angle of reflection = ?

Using law of reflection

=

= 25 deg

3)

some part of the ray gets reflected back and other part gets refracted.

For crown glass :

n_air = index of refraction of air = 1

n_crown = index of refraction of crown glass = 1.52

= Angle of incidence = 16.14 deg

= Angle of refraction = ?

Using Snell's law

n_air Sin = n_crown Sin

1 Sin = (1.52) Sin16.14

= 25 deg

= Angle of reflection = ?

Using law of reflection

=

= 16.14 deg