Index of refraction, dispersion, and resolving power of a prism spectroscope

Principle

The spectrometer-goniometer is used to determine the angle of deflection that light undergoes when passing a prism. The refractive index of a prism at the specific wavelength of a known spectral line can be determined by observation of the angle of least deflection of light of that spectral line effected by that prism, given that the angle between the planes of the prism is known. If this measurement is done for different spectral lines, the dispersion curve of the prism can be determined. Prisms made of different glass and a hollow prism that can be filled with different liquids are used to determine dispersion curves of different types of glass and different liquids. Further can be shown how the spectral resolving power of a prism spectrometer depends on the dispersion and size of a prism. For this an adjustable slit is used to restrict the useful width of the light beam. The effect on the resolving power of a restricted beam width is observed.

Benefits

• understand fundamentals of spectroscopy
• compact setup
• precise and reproducible results

Tasks

1. To adjust the spectrometer-goniometer.

2. To determine the refractive index of various liquids in a hollow prism.

3. To determine the refractive index of various glass prism.

4. To determine the wavelengths of the mercury spectral lines.

5. To demonstrate the relationship between refractive index and wavelength (dispersion curve).

6. To calculate the resolving power of the glass prisms from the slope of the dispersion curves.

7. Determination of the grating constant of a Rowland grating based on the diffraction angle (up to the third oder) of the high intensity spectral lines of mercury.

8. Determination of the angular dispersion of a grating.

9. Determination of the resolving power required to separate the different Hg-Lines. Comparison with theory

Learning objectives

• Maxwell relationship
• Dispersion
• Polarisability
• Refraction, Refractive index
• Prism
• Rowland grating
• Spectrometer
• Goniometer
•  Dielectric polarizability
• Relative electric and magnetic permissivity