Investigating Whether the Color of Light Incident on a Medium Affects Its Refractive Index

Investigating Whether the Color of Light Incident on a Medium Affects Its Refractive Index

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Investigating Whether the Color of Light Incident on a Medium Affects Its Refractive Index


Background – Refraction is the bending of light when it passes from
one medium to another. Refraction occurs because of the change in
density in the new medium which changes the amount of obstruction of
the light causing the light to deviate from its original path and take
a new, shortest one through the new medium. Refractive index is a
unique property of transparent and translucent materials. It is
governed by Snell’s law μ = Sin i / Sin r where i and r are the angles
of incidence and refraction respectively and μ is the refractive index
and is defined as “A property of a material that determines how fast
light travels through it.”1

Hypothesis – I believe that the refractive index of a transparent or
translucent medium is independent of the colour of light incident on
it. Light always travels in a straight line. When a ray of light
enters a medium at a certain angle, it is forced to bend because of
the change in density in the new medium and thus, a change in
obstruction. The ray will have to deviate from its original path and
find an alternate, short and straight way through the atoms of the new
medium. Any colour of light will have to follow this same path for the
shortest and straight way out of the medium, provided the incident
angle remains the same. This means that the new medium will bend any
colour of light at the particular angle of incidence, by the same
value producing the same angle of refraction. Since i and r will
remain constant, according to Snell’s law, μ will remain constant.

Apparatus – Ray box x 1

Perspex slab x 1

Light filters x 6 (violet, blue, green, yellow, orange, red)

Power pack x 1

Protractor x 1

Pencil

Ruler

Plain white paper

Variables - I will keep the angle of incidence constant.

I will change the colour of light incident on the Perspex.

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I will measure the angle of refraction.

I will derive the refractive index of the Perspex.

Plan – The plan is to let a beam of white light from the ray box fall
on the Perspex. It will be refracted. A normal will be drawn
perpendicular to the point where the light hits the Perspex slab.
Another normal will be drawn perpendicular to the point where the
light comes out from the Perspex. The incidence path and the refracted
path will be traced and the angle of incidence and refraction
calculated. Then, different filters will be placed in front of the
white beam and the same process will be carried out for different
colours for the same angle of incidence. In each case, μ will be
calculated.

Procedure –

* Draw the outline of the Perspex slab on the white paper.

* Tape the edges of the white paper to the table and the Perspex to
the white paper to prevent both from moving.

* Connect the ray box to the power pack, A.C. 12V.

* Introduce a plastic piece with a very thin slit to allow a very thin
beam of light in the slot in front of the ray box.

* Let the beam of white light be incident on the Perspex at 79°. This
angle should be with respect to the normal and not with respect to the
outline of the Perspex.

* Make a point where the beam hits the Perspex and trace the incident
path.

* Make a point where the beam comes out of the prism and trace the
path of the beam after coming out of the Perspex.

* Join both the dots to get the refracted ray.

* Measure the refracted angle and perform SnellÂ’s equation to get a
value of μ.

* Add light filters in front of the plastic piece to get thin beams of
different colours.

* Repeat the procedure.

* Change the angle of incidence to 60°.

* Repeat the same process and calculate the value of μ.

Results – The results are as follows:

Trial 1

i = 75°

r = 79°

μ = Sin i / Sin r

= Sin 75° / Sin 79°

= 0.984

Trial 2

i = 60°

r = 61.5°

μ = Sin 60° / Sin 61.5°

= 0.986

Conclusion – It can be seen from the results that the values of the
refractive index calculated in both trials are very close; there is a
very small difference between them. It may mostly be because of an
experimental error. It confirms the claim made in the hypothesis that
the refractive index is independent of the colour of light incident on
the medium.

However, the claim made in the hypothesis is wrong. Refractive index
does depend on the colour of the light incident on the medium, mainly
the wavelength. Scientific experiments have shown that colours of
light with a shorter wavelength are refracted more than a colour with
a longer wavelength, i.e. violet is bent the most and red is bent the
least. This can be explained by saying that with a shorter wavelength,
we have a greater frequency or more number of waves. When more number
of waves hit the medium, the part that hits the wave first is
refracted. Right after that, other waves follow up and force the waves
before them to refract quickly. This rush that is caused can be
imagined such that the waves want to refract quickly and thus push the
waves preceding them with a large force one after the other making the
preceding waves bend by relatively large angles. With waves of longer
wavelength and lower frequency, the rush created will be much less.
The number of waves hitting their preceding waves will be less because
the waves are placed over large distances. This will cause the waves
to bend at relatively smaller angles. Thus, for the same angle of
incidence, different colours will bend at different angles. This can
also be explained on the fact that if all colours bent at the same
angles, then dispersion of white light would never have taken place
and we would never have known that white light was a mixture of
several different colours. Because each colour bends at different
angles, white lightÂ’s components bend at different angles and give us
a spectrum of different colours.

Evaluation – The conclusion suggests that the hypothesis made was
incorrect. However, the results obtained support the claim made. This
suggests that there must have been errors in the experiment.

One possible source of error is that the ray of light coming out of
the ray box was not collimated despite the adjustment made. This
causes problems because I assumed the ray from the slit card to hit
the Perspex slab as parallel rays but they were not parallel. This
means that each end was of a different angle. However, this difference
between these angles would be very small because the width of the ray
was very small and using small angle approximation, the Sinus of the
two different angles would be very close to the value of the angles
themselves and thus, negligible.

Another source of error could be the point chosen on the ray of light.
Despite the small thickness of the ray of light, the light opened up
or diffracted more at the point it hit the slab. The centre of the ray
was chosen but there could be errors in judging the points. Since the
same points were taken for every colour in each trial, this counts as
a systematic error which can upset the results.

Other sources of error could be with the apparatus chosen. There could
have been faults with the filters i.e. they might not be true red or
true green for example. These differences will produce a light of a
different wavelength that may appear to be a common colour like red or
green but in reality, could be a shade of it. Again, this means that
it is very difficult to produce a true colour. It could have affected
the results because maybe with a true colour, different angles could
have been obtained which would have proven the hypothesis wrong.

Measurement uncertainties were not taken into account, mainly with the
protractor. This would certainly cause errors in the angles.

I would try to improve this experiment in many ways. First, I would
include measurement uncertainties in my results to obtain a precise
and accurate result. I would try to make the rays of light as
collimated as possible i.e. to try to make them as parallel to each
other as possible. This would ensure that there is negligible
difference in the angles at the two ends of the light. I would also
use a narrower slit to make the ray of light as thin as possible. This
would ensure that choosing a point on the ray is not very difficult. I
would also either bring the Perspex closer to the slab or the ray box
closer to the Perspex to minimise diffraction. I would do the
experiment for different colours in each trial, separately instead of
just on one

This would make results more accurate by having separate results. I
would also perform more number of trials to minimise random errors. I
might probably use more accurate filters or rather lasers of different
colours to have a monochromatic light than a polychromatic light since
they are collimated and diffract less than polychromatic beam of
light.


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1 Intel, Silicon Photonics Glossary – Glossary of terms relating to
Silicon Photonics.
http://www.intel.com/technology/silicon/sp/glossary.htm (updated 10th
April 2005, accessed 10th April 2005)
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