Dispersion and resolving power of a grating spectroscope

Principle

The diffracted light from a periodic line grating is observed with a goniometer. The diffraction angles of spectral lines in different orders of diffraction are measured for the spectral lines from a Hg spectral lamp. By using gratings with different grating constants the angular spectral dispersion in dependence on grating constant is determined.

The effect of the total number of grating lines taking part in the diffraction is observed by reducing the beam width with an adjustable slit and the diffraction on that slit is taken into account. The spectral resolving power of a grating with given grating constant and useful beam width is observed and compared with theoretical considerations. 

Benefits

• Understand fundamentals of spectroscopy
• Compact setup
• Precise and reproducible results

Tasks

1. Adjustment of the grating spectroscope 
2. Measure the diffraction angle for different wavelenght and order of diffraction 
3.  Measure the diffraction angle for different grating constants
4. Identify the mercury (Hg) spectral lines 
5. Determine the grating constant for known spectral lines 
6. Determine the angular dispersion in dependence on grating constant 
7. Observe the spectral resolving power with reduced beam width - when can spectral lines still be separated?

Learning objectives

• Maxwell relationship
• Dispersion
• Polarisability
• Refractive index
• Prism
• Rowland grating, Diffraction grating
• Spectrometer
• Goniometer
• Constructive and destructive interference
• Interference and diffraction on edge, slit, and grating 
• Spectral resolving power