Color and Spectra

Introduction:

The purpose of this experiment is to find the wavelengh of different color for the wavelength spectrum by applying the concept of constructive interference. The idea of the constructive interference is used because when the light source entered the slits, the distance through the upper slits and the distance through the lower slits are the same. Therefore, the wave fronts spread out from the upper slits and the lower slits are in phase. In this case, the upper slits and the lower slits are coherent. Since the width of the slits is much smaller than the distance from the light source to the slits, the equation used for this experiment is:

y_m=Rmλ/d

,so the equation for wavelength is:

λ= y_md/R

here λ is the wavelengh of the color on the spectruem, y_m is the width of the slit, d is the distance from the center to the first dark fridge, and R is the distance between the light source and the slits(linear diffraction grating ). The other method, witch actually has the same concept as the above one can also be applied to get the result of the wavelength. The two similar triangles are used to get the wavelength λ,where

λ/d=D/√(L²+D²)

after the equation is rearrange, the new equation for wavelengh is obtained:

λ= Dxd /√(L²+D²)

here, d is the width of the slits, L is the distace from the light soure to the slits(linear diffraction grating ), D is the distance from the central mexima to the first minima. As a result, it proves that the concept of constructive interference was applied.

The basic appartus for this experiment

Data and Calculations:

Distance from the light source to the grating : 1m			Wavelength Spectrum (nm)
			Violet	Blue	Green	Yellow	Red
			415	472.5	532.5	580	685
White	---------------		Violet	Blue	Green	Yellow	Red
500 lines for 1mm àym=2×10-6			Range(cm)
			18~22.5	22.5~24.2	24.2~27.5	27.5~30	30~38.5
If the wavelength has large difference: λ=mλ+λ0			Distance from light source to the middle of the range(cm)
			20.25	23.35	25.85	28.75	34.25
			Equation λ = dy/L
			Wavelength(nm)
			405	467	517	575	685

 Obtaining Wavelengh Uncertainty by plotting and get the slope:



After Uncertainty Equation was applied:

Wavelength(nm)
415	472.5	532.5	580	685
Wavelength with uncertainty(nm) Slope = 1.0334x
418.5	482.5	534	577	707

In this figure, it shows us that the wavelenght spectrum is formed when we view the light source through the linear diffraction grating

 Now the color of the light source was changed, the hydrogen tube and one unknown tube would be used as the light source and the different wavelengh would also be calculated. The idea of getting different color specturm is that different color has its particular path hence having a particular wavelength. The wavelength for that colar will superimpose in a constructive manner and thus different color would appear.Each path of each color would reinforce itself and also cancel other color's wavelengh at its position. Since the distance from the upper slits is still equal to the distance from the lower slits, it shows that the wave fronts are inphase as discussed earlier.

Data and Calculations:

Hydrogen Tube
Color	Violet	Green	Yellow		Red
Distance from the grating to the light source(cm)	19.9	22.1	27		31.6
Wavelength (nm)	398	442	540		632
	Unknown Gas #4 Tube
Color		Violet		Green	Red
Distance from the grating to the light source(cm)		23.4		27.2	33
Wavelength (nm)		468		544	600
	Actual unknown Gas-Neon
Color	Pink	Blue		Green	Red
Actual Wavelength (nm)	410	434		486	656

Conclusion and Discussion :

Based on the experimental results obtined from the white light, the final wavelenght with applying the uncertainty euation would be within 10 (nm) if the inital experimental result is not close to the actual value enough. Therefore, the results with uncertainty shows that with the concept of constructive interference and the concept of spectrumeter, the results satisfy that when light passes through the linear diffraction grating, the particle emitted by the light reaches its excited level and drops back to the ground level. When it goes back to its ground level, with the energy losing, or the energy being emitted to reach the excited level, it results in having lower energy and hence longer wavelength. Therefore, conclusively, the visible portion of the light (the range for the wavelength of those visible lights ) appears and forms different colors. It is also known as the specturm.  It can also be denoted as the absorption spectrum, which a series of dark lines corresponding to differen length of the wavelengths were constructed with the concept of interference.