13 Jul 2026

Resolving Power of a Prism

practical pg-i optics prism resolving-power

Aim

To determine the resolving power of a prism by observing two nearby spectral lines.

Apparatus

Spectrometer, high-dispersion prism, sodium or mercury lamp, narrow slit, collimator, telescope, and reading lens.

Experimental arrangement

The prism is mounted on the spectrometer table between the collimator and telescope; the slit and telescope are adjusted for sharp spectral lines.

Theory

Light entering a prism is refracted because its speed changes at the glass-air boundary. Since the refractive index depends on wavelength, two nearby wavelengths emerge at slightly different deviations. The instrument can distinguish the lines only when the two broadened images are sufficiently separated.

The resolving power of a prism is the ratio $R=\lambda/\Delta\lambda$, where $\Delta\lambda$ is the smallest wavelength separation that can just be distinguished. Two lines are considered just resolved when the maximum of one overlaps the first minimum of the other according to the Rayleigh criterion. A larger base angle, greater dispersion, and longer effective path in the prism improve resolution.

Observations

Spectral pair	Wavelengths (nm)	Observation
mercury yellow doublet	577.0, 579.1	just resolved
sodium doublet	589.0, 589.6	not resolved

For the mercury pair, $\lambda=578.05$ nm and $\Delta\lambda=2.1$ nm.

Result

The prism resolves the mercury yellow pair but does not resolve the closer sodium doublet under the present adjustment. The resolving power for the mercury pair is approximately $R=275$.

Viva Questions

1. What is resolving power? $R=\lambda/\Delta\lambda$.
2. Why is a narrow slit used? It reduces geometrical broadening of the spectral image.
3. What is the Rayleigh criterion? Two lines are just resolved when the principal maximum of one coincides with the first minimum of the other.