Determining Wavelengths Using Mercury Source

Sep 18, 2024

Experiment on Determining Wavelengths of Spectral Lines Using Mercury Source

Introduction

  • The experiment focuses on optics, specifically determining the wavelengths of spectral lines from a mercury source.
  • Two main apparatus used: Transmission Grating and Spectrometer.

Apparatus Overview

Source

  • Cabinet Structure: Houses the light source and includes a small slit for light to exit.

Spectrometer

The spectrometer has three main parts:

  1. Collimator

    • Contains a slit whose width can be adjusted using a screw.
    • A rack and pinion arrangement for focusing the distance between the slit and lens.
    • Two screws: one for locking and one for adjusting the horizontal level.

  2. Prism Table

    • Contains three screws for leveling the prism.
    • Spirit level used to ensure horizontal alignment.
    • A screw for height adjustment of the prism table; connected to a vernier scale for measurements.

  3. Telescope

    • Contains field ends and eyepiece with position adjustable via rack and pinion.
    • Used for observing the reflected image of the slit.

Scale of the Spectrometer

  • Fixed Scale: Below, immovable.
  • Movable Scale: Vernier measures angular separation, not length.
  • Additional screws for locking and fine adjustments of the telescope.

Experiment Setup

  • Positioning the spectrometer so that light enters the collimator.
  • Two observations:
    1. Adjustment of spectrometer
    2. Determination of angular deviations
  • Ensure the grating is perpendicular to the incident beam using a glass plate and 45-degree reflection principle.

Adjusting the Grating

  • Once the grating is aligned, set the telescope and collimator at 90 degrees.
  • Record readings when the grating is perpendicular to the incident beam, ensuring accurate positioning.

Spectrum Observation

  • Move the telescope to observe different colors of spectrum:
    • Indigo, Green, Yellow
  • Record readings for first-order spectrum on both left and right sides.

Readings Taken

  1. Indigo:
    • Left Side: Vernier 1: 28.7°, Vernier 2: 209.34°
    • Right Side: Vernier 1: 81.32°, Vernier 2: 261.18°
  2. Green:
    • Left Side: Vernier 1: 21.64°, Vernier 2: 202.14°
    • Right Side: Vernier 1: 88.58°, Vernier 2: 268.37°
  3. Yellow:
    • Left Side: Vernier 1: 19.58°, Vernier 2: 199.84°
    • Right Side: Vernier 1: 90.84°, Vernier 2: 270.63°

Calculating Angular Separations

  • Calculate differences for each color between left and right side readings to find angular separations (2θ) and then θ.
  • Average values derived:
    • Indigo: 52.50°
    • Green: 66.59°
    • Yellow: 71.03°

Wavelength Calculation

  • Formula: ( \lambda = \frac{E \sin(\theta)}{n} )
    • E: Grating element, determined by lines per inch.
    • Calculate wavelength for each color:
      1. Indigo: 4423 Å
      2. Green: 5489 Å
      3. Yellow: 5808 Å

Conclusion

  • Successfully performed the experiment to determine the wavelengths of spectral lines using a mercury source, confirming the expected values within a reasonable range for measured wavelengths.