Why does dispersion take place when light is passed through prism and not through glass slab?
Asked by: Kavita
A light ray is refracted (bent) when it passes from one medium to another at an angle and its
speed changes. At the interface, it is bent in one direction if the material it enters is
denser (when light slows down) and in the OTHER direction if the material is less dense
(when light speeds up). Because different wavelengths (colors) of light travel through a
medium at different speeds, the amount of bending is different for different wavelengths.
Violet is bent the most and red the least because violet light has a shorter
wavelength, and short wavelengths travel more slowly through a medium than longer ones do.
Because white light is made up of ALL visible wavelengths, its colors can be separated
(dispersed) by this difference in behavior.
When light passes through glass, it encounters TWO interfaces--one entering and the other
leaving. It slows down at the first interface and speeds back up at the second. If the two
interface surfaces are parallel to each other, as in a 'slab' of glass, all of the
bending (and dispersion) that takes place at the first interfaces is exactly reversed at the
second, 'undoing' the effect of the first interface; so although the emerging ray of
light is displaced slightly from the entering ray, it travels in the same direction as the
incoming ray and all wavelengths that separated at the first interface are re-combined.
If the second interface is NOT parallel to the first, as in a prism, the effects of the
first interface are NOT reversed and the colors separated at that interface continue
along different paths upon leaving the glass.
Answered by: Paul Walorski, B.A. Physics, Part-time Physics Instructor
Well, in fact, dispersion does occur when light
is passed through a glass slab - it is just harder
to observe that way. Lets summarize how this
Refraction of light when it passes from one medium
to the other obeys Snell's law, which states:
n1 sin(1) = n2 sin (2)
Where n1 and n2 are the indices of refraction
of the two media, and 1 and 2 is the angle
the ray of light makes with the normal to the
surface in the two media. The index of refraction
for air is (almost) 1, while for glass it is
about 1.5 (or so). So, when light enters a
medium with higher index of refraction, it will
be bent toward the normal, i.e. end up closer
to being perpendicular to the surface.
So far so good. But how does that explain the
dispersion of different colors of light? The
answer lies in n, the index of refraction. The
index of refraction is not a constant, but rather
varies with the frequency (hence, wavelength) of
the light involved. So, different colors are
bent by different amounts. So, in a prism, light
goes through two surfaces, which are not parallel
and as a result, every color exiting the prism
travels in a different direction - splitting up
clearly over a short distance.
Now, for a slab the situation is different. Since
the two surfaces are parallel, the direction of
any color light is not changed by going through
the slab - it is only offset by a small amount
(that's exactly why objects look displaced a
little when looked at through a glass slab). This
offset depends on the angle of incidence, the
index of refraction, and is directly proportional
to the thickness of the slab. As a result, every
color is offset by a very small amount with
respect to each other, and the color separation
is only observable at the edges, or if one uses a
very small spot of light, and a very thick slab
Answered by: Yasar Safkan, B.S. Physics, Ph.D. Candidate, MIT
'The most precious things in life are not those one gets for money.'