Refractive Index and Dispersion: Prism Spectrometer
OBJECTIVES:
The purpose of this experiment is to study the phenomenon of dispersion i.e. to
determine the variation of refractive index of the glass prism as a function of
wavelength and to compare the experimental data with the classical normal
dispersion function
EQUIPMENT:
glass prism, spectrometer, sodium and neon lamp
INTRODUCTION:
The dependence of the velocity of propagation of the wave on the properties of the
medium gives rise to the phenomena of refraction and reflection, which occur when a
wave crosses a surface separating two media, where the wave propagates with
different velocities. The reflection and refraction of waves that occur at surfaces of
discontinuity can be analyzed geometrically using the ray concept when no other
changes happen at the surface. This method is called wave geometry or ray tracing.
In particular, for electromagnetic waves in the visible and near visible regions, it
constitutes geometrical optics, which is a very important branch of applied physics. In
this way we are able to examine optical behavior that does not depend on the nature
of light, but only on the straight-line path it travels. Under the approximation of
geometrical optics we can say that although the light wave spreads as it moves away
from the source, it travels in the straight line.
Refraction is the bending of light that takes place at a boundary between two
materials having different indices of refraction (n1 and n2). Refraction is due to a
change in the speed of light as it passes from one medium to another. No bending of
the incident ray occurs if it strikes the boundary along the normal, which is a
construction line drawn perpendicular to the boundary at the point of incidence.
The incident ray is the ray approaching the boundary. It strikes the boundary at the
point of incidence. The refracted ray is the ray leaving the boundary through the
second medium. The reflected ray is the ray undergoing partial (or total) reflection at
the boundary. The angle of incidence α1 is the angle between the incident ray and
the normal. The angle of reflection α2 is the angle between the normal and the
reflected ray. The angle of refraction β is the angle between the normal and the
refracted ray.
Laws of Reflection and Refraction:
1. The directions of incidence, refraction and reflection ray are all in one plane,
which is normal to the surface of the separation of two media and therefore
contains the normal of the surface.
2. The angle of incidence is equal to the angle of reflection. That is
3. The ratio between the sine of the angle of incidence and the sine of the angle of
refraction is a constant (this ratio is constant for a particular wavelength and a
particular set of materials). This is called Snell's Law and it is expressed by
1
1 2
n
n
sin
sin = β
α
(2.a)
Subscript 1 is customarily used to represent the incident medium. Subscript 2
represents the refractive medium. The Equation (1) is valid regardless of the direction
in which light is traveling through the two media.
The constant ni is called the absolute index of refraction of the medium (i). We define
it to be the ratio of the speed of the light in vacuum c to the speed of the light in that
medium Vi (i.e. ni=c/Vi).
Snell's Law can be written also in the form:
2
1
21
1
V
V
n
sin
sin = = β
α , (2.a)
where n12 is called the relative index of refraction (index of refraction of the medium
(2) relative to the medium (1)), being the ratio of the refractive indices and the ratio of
the speeds of light in two media. Its numerical value depends on the nature of the
wave and on the properties of two media.
If light is traveling from a less refractive medium to a more refractive medium (i.e. n2
> n1), the refracted ray will be bent towards the normal (Figure 1). When a light ray
travels from a more dense (with higher refractive index) to a less dense optical
material, the ray is bent away from normal.
A dispersive medium is one in which different wavelengths λ of light have slightly
different indices of refraction n (i.e. n=n(λ)).
Water, glass, transparent
plastics, and quartz are all
dispersive materials.
Generally, in the case of
normal dispersion, the
shorter wavelengths travel
with slightly smaller wave
velocities than do longer
waves (i.e. refractive index
is decreasing with a
wavelength).
This phenomenon is
characteristic for a
transparent media. As an
example, the index of
refraction for quartz that
varies with the wavelength
in the visible and near-visible region is shown in Figure 2.
In the case of light absorption the anomaly dispersion is observed, what means that
refractive index is increasing as a function of the wavelength.
When a wave is refracted into a dispersive medium which index of refraction
depends on the wavelength, the angle of refraction also depends on the wavelength.
If the incident wave, instead of being monoch