Pankaj Samant 10-b

PHYSICS PROJECT
REFLECTION & REFRACTION
 Light
Light is electromagnetic radiation that has properties of waves. The electromagnetic spectrum can be divided into
several bands based on the wavelength of the light waves. As we have discussed before, visible light represents a
narrow group of wavelengths between about 380 nm (1 nm = 10-9 m) and 730 nm.

Our eyes interpret these wavelengths as different colors. If only a single wavelength or limited range of
wavelengths are present and enter our eyes, they are interpreted as a certain color. If a single wavelength is
present we say that we have monochromatic light. If all wavelengths of visible light are present, our eyes interpret
this as white light. If no wavelengths in the visible range are present, we interpret this as dark.
 Interaction of Light with Matter
Velocity of Light and Refractive Index
The energy of light is related to its frequency and velocity as follows:

E = hυ = hC/λ

where E = energy, h = Planck's constant, 6.62517 x 10-27 erg. Sec, υ = frequency,

C = velocity of light = 2.99793 x 1010 cm/sec, λ = wavelength

The velocity of light, C, in a vacuum is 2.99793 x 1010cm/sec. Light cannot travel faster than this, but if it travels
through a substance, its velocity will decrease. Note that from the equation given above-
C = υλ
The frequency of vibration, υ, remains constant when the light passes through a substance. Thus, if the velocity,
C, is reduced on passage through a substance, the wavelength, λ, must also decrease.
We here define refractive index, n, of a material or substance as the ratio of the speed of light in a vacuum, C, to
the speed of light in a material through which it passes, Cm.
n = C/Cm
Note that the value of refractive index will always be greater than 1.0, since Cm can never be greater than C. In
general, Cm depends on the density of the material, with Cm decreasing with increasing density. Thus, higher
density materials will have higher refractive indices.
The refractive index of any material depends on the wavelength of light because different wavelengths are
interfered with to different extents by the atoms that make up the material. In general refractive index varies
linearly with wavelength.
Materials can be divided into 2 classes based on how the velocity
of light of a particular wavelength varies in the material.

Materials whose refractive index not depend on the direction that the light travels are called isotropic materials.
In these materials the velocity of light does not depend on the direction that the light travels. Isotropic materials
have a single, constant refractive index for each wavelength. Minerals that crystallize in the isometric system, by
virtue of their symmetry, are isotropic. Similarly, glass, gases, most liquids and amorphous solids are isotropic.

Materials whose refractive index does depend on the direction that the light travels are called anisotropic
materials. These types of materials will have a range of refractive indices between two extreme values for each
wavelength. Anisotropic materials can be further divided into two subclasses, although the reasoning behind
these subdivisions will become clear in a later lecture.

Minerals that crystallize in the tetragonal and hexagonal crystal systems (as well as some plastics) are uniaxial
and are characterized by 2 extreme refractive indices for each wavelength.

Minerals that crystallize in the triclinic, monoclinic, and orthorhombic crystal systems are biaxial and are
characterized by 3 refractive indices, one of which is intermediate between the other two.
Air, since it is a gas, is isotropic.

The refractive index of air is usually taken as 1.0, although its true value is 1.0003.
 Reflection and Refraction of Light
When light strikes an interface between two substances with different refractive indices, two things occur. An
incident ray of light striking the interface at an angle, i, measured between a line perpendicular to the interface
and the propagation direction of the incident ray, will be reflected off the interface at the same angle, i. In other
words the angle of reflection is equal to the angle of incidence.

If the second substance is transparent to light, then a ray of light will enter the substance with different refractive
index, and will be refracted, or bent, at an angle r, the angle of refraction. The angle of refraction is dependent
on the angle of incidence and the refractive index of the materials on either side of the interface according to
Snell's Law:
ni sin (i) = nr sin (r)

Note that if the angle of incidence is 0o (i.e. the light enters perpendicular to the interface) that some of the light
will be reflected directly back, and the refracted ray will continue along the same path. This can be seen from
Snell's law, since sin(0o) = 0, making sin (r) = 0, and resulting in r = 0.
There is also an angle, ic, called the critical angle for total internal
reflection where the refracted ray travels along the interface between
the two substances.

This occurs when the angle r = 90o. In this case, applying Snell's law:

ni sin (ic) = nr sin (90o) = nr [since sin (90o) = 1]

sin (ic) = nr/ni

 Dispersion of Light
The fact that refractive indices differ for each wavelength of light produces an effect called
dispersion. This can be seen by shining a beam of white light into a triangular prism made
of glass. White light entering such a prism will be refracted in the prism by different angles
depending on the wavelength of the light.

The refractive index for longer wavelengths (red) are lower than those for shorter
wavelengths (violet). This results in the a greater angle of refraction for the longer
wavelengths than for the shorter wavelengths. (Shown here are the paths taken for a
wavelength of 800 nm, angle r800 and for a wavelength of 300 nm, angle r300 ). When the
light exits from the other side of the prism, we see the different wavelengths dispersed to
show the different colors of the spectrum.
 Absorption of Light
When light enters a transparent material some of its energy is dissipated as heat energy, and it thus looses some of
its intensity. When this absorption of energy occurs selectively for different wavelengths of light, they light that
gets transmitted through the material will show only those wavelengths of light that are not absorbed. The
transmitted wavelengths will then be seen as color, called the absorption color of the material.

For example, if we measure the intensity of light, Io, for each

wavelength before it is transmitted through a material,
and measure the intensity, I, for each wavelength after it has
passed through the material, and plot I/Io versus wavelength
we obtain the absorption curve for that material as shown
here. The absorption curve (continuous line) for the material
in this example shows that the light exiting the material will
have a yellow-green color, called the absorption color.
An opaque substance would have an absorption curve such
as that labeled "Dark", i.e. no wavelengths would be
transmitted.

Sunlight, on passing through the atmosphere has absorption

curve as shown, thus we see it as white light, since all
wavelengths are present.