Physics Concept: Light Reffraction on Plan Parallel Glass

(1)

When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, as shown in Figure 35.10, part of the energy is reflected and part enters the second medium. The ray that enters the second medium is bent at the boundary and is said to be refracted. The incident ray, the reflected ray, and the refracted ray all lie in the same plane. The angle of refraction depends on the properties of the two media and on the angle of incidence through the relationship as follow:

where v1 is the speed of light in the first medium and v2 is the speed of light in the second medium.

The path of a light ray through a refracting surface is reversible. For example, the ray shown in Figure 1 bellow travels from point A to point B. If the ray originated at B, it would travel to the left along line BA to reach point A, and the reflected part would point downward and to the left in the glass.

Figure 1. (a) A ray obliquely incident on an air–glass interface. The refracted ray is bent toward the normal because v₂ > v₁. All rays and the normal lie in the same plane. (b) Light incident on the Lucite block bends both when it enters the block and when it leaves the block.

From Equation (1), we can infer that when light moves from a material in which its speed is high to a material in which its speed is lower, as shown in Figure 2, the angle

of refraction &2 is less than the angle of incidence &1, and the ray is bent toward the normal. If the ray moves from a material in which light moves slowly to a material in which it moves more rapidly, as illustrated in Figure 2 θ₂ is greater than θ₁, and the ray is bent away from the normal.

Figure 2. (a) When the light beam moves from air into glass, the light slows down on entering the glass and its path is bent toward the normal. (b) When the beam moves from glass into air, the light speeds up on entering the air and its path is bent away from the normal.

The behavior of light as it passes from air into another substance and then reemerges into air is often a source of confusion to students. When light travels in air, its speed is 3.00 x10⁸ m/s, but this speed is reduced to approximately 2 x10⁸ m/s when the light enters a block of glass. When the light re-emerges into air, its speed instantaneously increases to its original value of 3.00 x10⁸ m/s. This is far different from what happens, for example, when a bullet is fired through a block of wood. In this case, the speed of the bullet is reduced as it moves through the wood because some of its original energy is used to tear apart the wood fibers. When the bullet enters the air once again, it emerges at the speed it had just before leaving the block of wood.

(2)

In general, the speed of light in any material is less than its speed in vacuum. In fact, light travels at its maximum speed in vacuum. It is convenient to define the index of refraction n of a medium to be the ratio:

From this definition, we see that the index of refraction is a dimensionless number greater than unity because v is always less than c. Furthermore, n is equal to unity for vacuum.

(3)

Then, the experimental formula that was discovered by Willebrord Snell is:

n₁ sin θ₁ = n₂ sin θ₂

(4)

and for finding the translation of the refracted light we use formula:

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