13 Jul 2026

Dispersive Power and Cauchy Constants of a Prism

practical ug-iii optics prism dispersion

Aim

To determine the dispersive power and the Cauchy constants of a prism using mercury spectral lines.

Apparatus

Spectrometer, glass prism, mercury vapour lamp, and reading lens.

Apparatus image

Spectrometer and prism arrangement for measuring spectral-line deviations.

Theory

The refractive index depends on wavelength. In the visible region Cauchy’s formula is

\[\mu=A+\frac{B}{\lambda^2}.\]

The dispersive power is

\[\omega=\frac{\mu_F-\mu_C}{\mu_D-1},\]

where $F$, $D$, and $C$ denote the blue, yellow, and red reference lines.

Observations

Line	Wavelength (nm)	Minimum deviation	Refractive index
$F$	486.1	$41^\circ52’$	1.528
$D$	589.3	$39^\circ00’$	1.520
$C$	656.3	$38^\circ12’$	1.514

Prism angle: $A=60^\circ$.

Calculation

\[\omega=\frac{1.528-1.514}{1.520-1}=0.0269.\]

Using wavelengths in micrometres and the $D$ and $C$ lines,

\[1.520=A+\frac{B}{0.5893^2},\qquad 1.514=A+\frac{B}{0.6563^2}.\]

Solving gives $A=1.483$ and $B=0.0129\,\mu\text{m}^2$.

Result

\[\boxed{\omega=0.0269},\qquad \boxed{A=1.483,\;B=0.0129\,\mu\text{m}^2}.\]

Precautions

1. Allow the mercury lamp to warm up before taking readings.
2. Identify each spectral line carefully.
3. Use the same prism face while comparing deviations.
4. Take readings on both verniers and use their mean.

Viva Questions

1. What is dispersion? It is the separation of polychromatic light into its component wavelengths.
2. Which colour is deviated most by glass? Violet, because its refractive index is greatest.
3. What does the constant $B$ indicate? It measures the wavelength dependence of refractive index in Cauchy’s approximation.
4. Why is the $D$ line used in dispersive power? It is a standard reference near the middle of the visible spectrum.

Maxima Code

Download the Maxima calculation file.