Diffraction Grating Analysis and Laser Wavelength Measurement

Study of Diffraction Phenomena and Light Wavelengths

Objectives

• To determine the emission wavelength of a laser using a diffraction grating with an electromagnetic wave.
• To determine the wavelength of each color of white light using a diffraction grating.
• To determine the emission wavelength of the laser based on the phenomenon of diffraction of an electromagnetic wave.

Planning

The diffraction grating is a device that separates light into its components. Two types exist: reflection gratings and transmission gratings. A transmission diffraction grating is built by parallel lines equally spaced on the flat surface of a glass plate, while a reflection grating uses a metal surface. These slots scatter light; the spaces between the grooves behave like slits.

Part I: Laser Wavelength Measurement

1. Place a lamp (initially off) and the diffraction grating, then observe the screen. A series of maxima and minima were formed.

2. Measure the distance between the central point and the first maximum. Measure the distance between the grating and the screen to calculate the angle.

Data and Calculations:

• d = 0.000125 m
• sin θ ≈ tan θ = 0.004 / 0.815 = 0.0049 (m) (using the triangle method)
• Formula: d sin θ = mλ
• λ = (0.000125 * 0.0049) / 1 = 612 × 10⁻⁹ m

Part II: White Light Spectrum Analysis

1. Replace the laser with a white light source.

2. Repeat the measurements for each color clearly perceived on the screen to determine their wavelengths.

L = 0.0013 m, d = 1.6 × 10⁻⁶ m

• Violet: 14.93º | 4.1 × 10⁻⁷ m
• Blue: 16.5º | 4.5 × 10⁻⁷ m
• Green: 18.43º | 5.05 × 10⁻⁷ m
• Orange: 20.13º | 5.5 × 10⁻⁷ m
• Yellow: 21.25º | 5.79 × 10⁻⁷ m
• Red: 22.7º | 6.17 × 10⁻⁷ m

The phenomenon of diffraction occurs when obstacle dimensions are comparable with the wavelength, resulting in a distortion of wave propagation.

Part III: Helium-Neon Laser Diffraction

This experiment utilizes a Helium-Neon (He-Ne) laser as a plane wave source, which is monochromatic and coherent. This radiation is incident on a slit, obtaining a diffraction pattern.

Calculations:

• Formula: b sin(θm) = mλ
• b = 0.00004 m
• sin θ ≈ tan θ = 0.0159 (using the proposed formula)
• λ = (0.00004 * 0.0159) / 1 = 636 × 10⁻⁹ m

Conclusions and Applications

We conclude that in Parts I and III, where we worked with the same laser, there is a small difference between the calculated lengths. However, both values are close to the reference laser wavelength of 650 × 10⁻⁹ m. The small error is due to measurement difficulties. In Part II, we obtained wavelength values for each color of the visible spectrum, matching the standard reference values for each color.