Physics Lab Report

Title:

Estimating the wavelength of light using a diffraction grating

Date:

28/09/211

Apparatus:

Ray box without lens, meter rules x2, diffraction grating with 300 lines per mm, voltage supply for ray box

Theory: Diffraction grating (transmission grating) is a sheet of glass plate with a large number of equally fine, closely spaced parallel lines ruled.

In the grating, each narrow slit acts as a source of light diffracted through a large angle. When the plane waves of monochromatic light with wavelength λ fall on the grating with grating space d, secondary wavelets come from successive slits with angle θ to the incident beam direction will reinforce together in that direction. Path difference between any two adjacent rays is dsinθ, given that the distance from retina is much larger than the slit width.

Equation d sinθ = nλ can also be applied when a white light source is used, which instead is a spectrum of light consisting different frequency light rays. When it is incident normally on the diffraction grating, several coloured spectra are observed on the either side of the normal.

At the middle is the zero-order fringe, which is white in colour. At this fringe, all frequencies of light has path difference = 0 λ , . They coincide together, giving a combined white colour.

Higher orders of light fringes will appear as continuous spectrum with red light observed at outer edge and violet light observed in inner edge. That is because violet light has a smaller λ than red one, giving a smaller diffraction in the same order. Thus they appear closer to the central spectral line. Dispersion of the diffraction band is also inversely proportional to the grating space d

by the theory d sinθ = nλ. Therefore through a finer grating, higher order pattern can be observed in a higher resolution. However overlap of different order spectrum should be avoided by limiting the fineness of grating used, as greater error will arise. Experimental Set-up

Using equation d sinθ = nλ, by measuring angle θ and order of spectrum, wavelength of different coloured light easily. This set-up is a good method for measuring wavelength of light as it only requires few apparatus commonly found in laboratories and give sharp and bright fringes. Procedures 1. Two meter rules were placed on the bench to form a ‘T’. 2. A grating was held against the end of one rule. It was used to view the vertical filament of a ray-box lamp about 1 to 2 meters away. 3. A pencil was moved along the second ruler until it is in line with the middle of the blue colour of the first order spectrum. Distance x was measured. The pencil was moved to coincide with the green and red colours in turn. 4. With d sinθ = n λ, where n = 1 for first order spectrum, the wavelengths of different colours were calculated.

Data Blue

Green

Red

x/cm

13.5

16.0

21.5

tanθ

0.135

0.160

0.215

θ/°

7.69

9.09

11.9

sinθ

0.134

0.158

0.210

λ =dsinθ /nm

446

527

701

Standard mean λ/nm

460

550

670

Therefore, Percentage error of blue light λ measured: (460-446)/460 = 3.04% Percentage error of green light λ measured: (550-527)/527 = 4.18% Percentage error of red light λ measured: (701-670)/670 = 4.42% Discussion A. Sources of error: 1. Error in determination of the position of the fringes as the pattern exists as a band instead of discrete fringes. 2. Misplaced and mis-determined meter rules and middle of rule. 3. Interference of external light source diffraction grating with the original pattern, disrupting data. B. Precautions: 1. The light source should be placed 1-2 meters away so that parallel incident light beam emitted is ensured. 2. Filament of the lamp should be point directly to the middle of the ruler. 3. Position of light band in both sides should be measured to obtain a fairer result and reduce error due to tilted horizontal meter used. C. Improvements 1. Measure wavelength of light source by using a spectrometer. 2. Repeat the experiment results to obtain a more accurate result. Conclusion Wavelength of blue light is 446nm, with percentage error of 3.04% Wavelength of red light is 527nm, with percentage error of 4.18% Wavelength of red light is 701nm, with percentage error of 4.42%