Refraction of Light

Refraction of Light

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Refraction of Light

Aim:

To find a relationship between the angles of incidence and the angles
of refraction by obtaining a set of readings for the angles of
incidence and refraction as a light ray passes from air into perspex.

Introduction:

Refraction is the bending of a wave when it enters a medium where it's
speed is different. The refraction of light when it passes from a fast
medium to a slow medium bends the light ray toward the normal to the
boundary between the two media. The amount of bending depends on the
indices of refraction of the two media and is described quantitatively
by Snell's Law. (Refer to diagram below)

The index of refraction is defined as the speed of light in vacuum
divided by the speed of light in the medium. In this experiment, the
index of refraction for the perspex is 1.50.

Snell's Law relates the indices of refraction of the two media to the
directions of propagation in terms of the angles to the normal. It
refers to the relationship between the different angles of light as it
passes from one transparent medium to another. When light passes from
one transparent medium to another, it bends according to Snell's law
which states:

[IMAGE]

where:
n1 is the refractive index of the medium the light is leaving,
n2 is the refractive index of the medium the light is entering,
sin 2 is the is the incident angle between the light ray and the
normal to the medium to medium interface, sin 1 is the refractive
angle between the light ray and the normal to the medium to medium
interface.

Definitions:

Angle of incidence: The angle made between an incident ray and the
normal to the surface that it strikes.

Angle of refraction: The angle made between the reflected ray and the
normal to the surface that it strikes.

Medium: The substance carrying a mechanical wave.

Refraction: The bending of the direction of travel of light as it

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enters a medium of different optical density.

Hypothesis:

Due to the theory that light bends when it passes from a less dense
medium to a denser medium, the light ray from the light box will bend
as it goes from the air into the perspex. Hence refraction of light
will be seen.

Equations/Units to be used:

· Sin i

· Sin r

· Sin i/ sin r (Snell's law)

· Critical angle (sin Ic = sin i/ sin r)

Variables:

Dependent Variable: Angle of incidence

Independent Variable: Angle of refraction

Controlled Variables:

· Material of perspex

· Intensity of light

· Frequency of light (i.e. Colour)

· Positioning of light on perspex

· Temperature of environment

· Type of perspex

· Surface on which experiment is conducted

Materials/Apparatus:

· Semi-circular perspex

· Light box

· Protractor

· Power supply

Reasons for choosing apparatus:

· Semi-circular perspex: only one point of refraction, and is more
denser than air, so that refraction will be able to be seen

· Colour of light: Normal light from the light box, so that the angle
of refraction could be seen better

· Light box: To obtain a beam of narrow light

· Protractor: To mark the incident angles

· Power box: To supply power to the light box

Safety Issues

· Avoid looking directly into the light source as this is harmful for
the eyes.

· Be careful of electricity

Method:

1) Mark and label points with a light pencil, of the various angles to
be measured. (Use a protractor)

2) Place the semicircular perspex block within the contours of the
semicircle drawn on the grid provided.

3) Shine a single ray from the ray box along the 10 degrees line and
mark the position of the refracted ray with a dot and the
corresponding alphabetical letter.

4) Do likewise for the rest of the lines with the assigned degree
value.

5) Remove the perspex block and draw lines to mark each refracted ray.

6) Measure the angles of refraction with the protractor and record
them onto the Results Table provided.

7) Do so for the rest of the Results Table.

[IMAGE]

How variables were kept constant:

The variables were kept constant by ensuring that they were
controlled. The most important variable that was to be controlled was
the positioning of light source, so that the light passed through the
centre of the perspex.

Difficulties encountered and how they were overcome:

· Accuracy of angles: used a protractor to measure

· Accuracy of refractive angles as the beam thickened as it passed
through the perspex: measured and marked a point on the grid as
closely as possible to the narrowest part of the light ray.

· Ensuring that the light went through the centre of the perspex:
repeated each angle 2-3 times to be sure of the results acquired

· Keeping the perspex stable: one person held the perspex while
another marked the points.

Results:

The results obtained were as accurate as possible, and covered a range
of angles, from 0 degrees to 80 degrees and not above that, as the
light ray would have been reflected. Also, the results obtained were
narrowed to + or - each side of the result. Lastly, the results from
three other students in the class were compared and then averaged to
ensure accuracy.

Angle of Incidence

Angle of Refraction

Average

Sin Incidence

Sin Refraction

sin i/sin r

0

0

0

0

0

0

0

0

0

10

7

7

6

7

7

0.174

0.116

1.503

20

13

12

13

14

13

0.342

0.226

1.513

30

19

22

20

20.5

19

0.5

0.327

1.528

40

25

25

24

24.5

25

0.643

0.416

1.547

50

31

31

31

32

31

0.766

0.515

1.487

55

33

31.5

32

32.5

33

0.819

0.545

1.504

60

35

33

35

35

35

0.866

0.574

1.510

65

37

37

36

35

37

0.906

0.602

1.516

70

39

38

40

37

39

0.94

0.629

1.493

75

40

39.5

41

41

40

0.966

0.643

1.503

80

42

43

42

44

42.5

0.984

0.656

1.500

*All results to 3 significant numbers Average: 1.506

Analysis of results:

The data collected relates to the aim, as the angle of incidence and
the angle of refraction, are obtained and were able to be used, to
find the relationship between both sets of results.

Graphs:

[IMAGE]

[IMAGE]

Equations:

Snell's Law

[IMAGE]

Snell's law gives the relationship between angles of incidence and
refraction for a wave impinging on an interface between two media with
different indices of refraction. The law follows from the boundary
condition that a wave is continuous across a boundary, which requires
that the phase of the wave be constant on any given plane, resulting
in

[IMAGE]


where [IMAGE]and [IMAGE]are the angles from the normal of the incident
and refracted waves, respectively.

Evaluations:

The values obtained for sin i/ sin r can all be rounded of to 1.50,
which is a constant, according to Snell's Law. This value is called
the absolute refractive index, which is constant for a certain object.

From the results table, it can be seen that the values for the
absolute refractive index of the perspex is approximately 1.50, which
is also the theoretical value for perspex.

These values were obtained by recording the points at which the light
ray bent, from air into the perspex. Hence, the constant for the
perspex was able to be calculated through Snell's Law, which states
that the sine of the incident angle divided by the sine of the
refractive angle will always give a constant, which is the absolute
refractive index of the material being experimented with. These values
also help to prove the aim, of finding a relationship between the
incident and refractive angles. Also, from the graph of the sin i over
sin r forms a straight line which allows us to find the gradient,
using the formula on the previous page. This helps to prove that the
gradient of the line is the same as the constant give by Snell's law.
However, when the graph of the incident angle over the refractive
angle is plotted, it results in a curve. Hence, the gradient cannot be
calculated. This proves that Snell's law is correct.

Lastly, using Snell's law, it can be determined that when the angle of
incident is zero degrees, the angle of refraction will also be zero
degrees. However, as the incident angle increases beyond the critical
angle and the refracted angle increases beyond 90 degrees, the
refracted ray is reflected back into the perspex, into the same plane
as the incident angle. This phenomenon is called total internal
reflection. This too can be calculated using Snell's law by setting
the refraction angle equal to 90°.

Inferences:

Limitations of apparatus and measuring equipment:

· Thick beam coming out from perspex, making it difficult to mark an
accurate point for the refractive angle.

· The protractor, only measuring to an accuracy of 1 degree, which may
cause the results to be slightly inaccurate.

· Thick refractive light ray which may have cause a difference of
almost 3 degrees.

· The ray of light passing right through the middle of the perspex.

Uncertainty of data and calculations:

· Making precise, exact line of the light rays

· Parallax error

· Estimation of where to draw point

Expected and derived relationships or physical values:

· The expected result for the relationship between the incident angle
and the refracted angle is a constant, 1.50 which is the relative
index for the perspex. The derived results are quite accurate, due to
the result being obtained and averaged out by comparing the results of
three other people. However, the result can be further improved by
using a grid that has the protractor printed on it. This would make it
easier, to read the angle of both the incident and refracted rays.

Conclusion:

The investigation of the relationship between the incident angle and
the refracted angle was a success. The absolute refractive index of
perspex was proven to be 1.50, although there were slight differences
in the results. Also, the investigation proved that Snell's law is
correct and that when light passes through a medium that is denser, it
bends (refraction). Also, the gradient, of any graph plotted for sin i
over sin r for particular material, results in a constant, which is
its relative index.


Bibliography:

1. http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/refr.html
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