Tuesday, June 14, 2011

Basic Physics (Light and Optics) - Pt. 17

We now begin the basic physics approach to light and optics, starting with one of the most fundamental investigations: that of refraction. In particular, we are interested in confirming Snell's Law, depicted in the top diagram. Here, the basic principle of refraction is that light, when passing from a less dense to a more dense medium (e.g. going from air to glass) will bend or change its direction. The direction will change on entering, then change again on exiting - since the latter case reverses the media (from more dense to less dense). The experimental design shown (Fig. 2) is one of the favorites used both at Harrison College Physics Dept. and when I taught 1st year Space Physics lab at the University of Alaska.

In the top diagram (Fig.1) n1 and n2 refer to refractive indices, defined as:

n1 = c/v1 and n2 = c/ v2

thus, n1 is the refractive index for air, and n2 the index for glass. If we require:

n1 v1 = n2 v2 then we can also write:

n1/n2 = v2/v1

in other words, the ratio of the refractive index in the more dense medium to the refractive index in the less dense medium is the ratio of the velocity of light in the more dense medium to the value in the less dense medium. Taking into account the two angles: Θ1 = angle of incidence, and Θ2 = angle of refraction, we may write:

n1 sin Θ1 = n2 sin Θ2

which is Snell's law.

The experimental set up is shown in Fig. 2. Here we set a glass plate or rectangular block on a sheet of A4 paper (toward the center) then use two pins to define the incident ray with respect to the normal (N) to the top of the block. (The normal line is carefully extended into the paper to more easily construct the rays.) We then use a 3rd and 4th pin to identify the exit ray from the lower portion of the glass block, and reference the angle r2 carefully by line of sight. Once the incident ray and emergent ray are validated, it is possible to complete the other measurements, for i1 and r1 and then for i2 and r2. By Snell's law then:

sin i/ sin r = v1/v2 = n

and it should be possible to obtain the index of refraction of the glass block.

Example problem:

In the experiment set up from Fig. 2, a student measures angle i1 = 60 degrees and r1 = 30 degrees. Find the experimental value of n for the block.

We have:

sin i1/ sin r1 = n


sin (60)/ sin (30) = n

or n = ([3]^½/ 2/ 1/2= [3]^½ = 1.73

Other problems:

1) For the same set up and experiment, obtain the values the student should get for the angles i2 and r2 for the emergent ray if his results are to be consistent.

2)If the speed of light in air is 300,000 km/sec what is the speed in a substance with refractive index 1.74?

3)Light in air has a wavelength of 0.0000589 cm. What would the wavelength be in water for which n(w) = 4/3.

4) When the angle i1 is equal to π/2, i2 is equal to what is called the critical angle. For this case: sin(π/2) = 1 so: 1 = n sin (i2).

If the index of refraction of a piece of extra dense flint glass is 1.60, would the critical angle be greater or less than 60 degrees?

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