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Color and the Wavelength of Light
- When Young did his double slit experiment, he determined the wavelengths for various colors of light:
- red - 6.5 X 10-7 m
- blue - 4.5 X 10-7 m
- Light that passes through a prism or diffraction grating, is separated into its colors because each color has a different wavelength.
- Dispersion - the breaking up of light into its colors.
- All frequencies in a vacuum have the same speed (3.00 X 108 m/s).
- We learned previously that the different colors of light have different speeds in some media (dispersive media).
- Since:
It follows that different colors of light (frequencies) have different indices of refraction.
e.g. for crown glass, violet has an absolute index of refraction of 1.53, but red
light has an absolute index of refraction of 1.51.
- As discussed before, incandescent sources of light will not produce interference patterns because:
- When one atom emits light, it is not likely that other atoms will emit light with the same phase.
- There is no regular pattern of repetition of phases and so any interference pattern will be constantly changing (therefore not visible).
- Monochromatic light - light of only one color.
- One frequency
- One wavelength
- Produced by lasers.
- Two lasers can produce interference patterns unlike incandescent sources.
- Young’s method however, is still the best.
Diffraction of Light From a Single Slit
- Whenever waves encounter a barrier with an opening in it, diffraction occurs.
- Interference also occurs
- The interference pattern consists of:
- Central Maximum - bright central region in the pattern.
- Secondary Maxima - less intense areas of light separated by dark regions of destructive interference on either side of the central maximum.
- The pattern forms because:
- There is more than one point in the slit.
- Each point behaves as a point source for waves radiating our in the direction of wave movement.
- The many circular waves from the many points, interfere with each other to produce the pattern.
- S1P1 = S2P1 and S3P1 = S4P1 etc. This results in the waves from the different points in the slit always arriving at P1 in phase. This produces constructive interference at P1. This constructive interference produces the central maximum.
- S1P1 is not = S2P1 and S3P1 is not = S4P1 etc. Therefore, for points on either side of the central maximum, since path lengths are not the same, the waves that arrive at these points on the screen (P1, P2, P3, P4, etc.) will not necessarily be in phase.
- If the path difference is a whole number of wavelengths, then constructive interference occurs.
- If the path difference is not a whole number of wavelengths, then destructive interference occurs.
- If S2P1 - S1P1 = nl, then constructive interference.
- If S2P1 - S1P1 = (n- 1/2)l, then destructive interference occurs.
- It is this difference in path length, being equal to a whole number of wavelengths or not, that results in the alternating bright and dark lines on either side of the central maxima.
- There are a number of equations that describe the pattern seen from a single slit. They are:
- To find the wavelength of the light, there are two other equations that can be used:
- The central maximum has a width that is twice the others (twice as wide as the adjacent minima).
- L must be large if the screen is flat. If L is not large, then the screen should be curved.
- Single slit interference is explained well by the wave model of light.
- With the double slits in Young’s experiment, each slit produces a single slit interference pattern
- What is seen on the screen is the interference pattern between the two central maxima.
- Interference between secondary maxima is usually too dim to see (can be made visible if wider slits are used).
November 21, 2013
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