Prism Refraction

I. Purpose

The purpose of the experiment are:

1. Determining the minimum deviation angle of each component of visible

light, exactly for red light and violet light.

2. Determining the magnitude of prism’s index of refraction.

II. Apparatus

There are several apparatus which used in this experiment, such as

follow:

1. Triangle prism,

2. Collimator,

3. Protractor (SSD: 1.0o) and ruler (SSD: 0.1 cm),

4. Coloring needles

5. HVS paper

6. Graphic paper

7. Pencil

8. Ruler

III. Base Theory

In optics, a prism is a transparent optical element with flat, polished

surfaces that refract light. The exact angles between the surfaces depend on

the application. The traditional geometrical shape is that of a triangular prism

with a triangular base and rectangular sides, and in colloquial use "prism"

usually refers to this type. Some types of optical prism are not in fact in the

shape of geometric prisms. Prisms are typically made out of glass, but can be

made from any material that is transparent to the wavelengths for which they

are designed.

A prism can be used to break light up into its constituent spectral colors

(the colors of the rainbow). Prisms can also be used to reflect light, or to split

light into components with different polarizations.

Light changes speed as it moves from one medium to another (for

example, from air into the glass of the prism). This speed change causes the

light to be refracted and to enter the new medium at a different angle

(Huygens principle). The degree of bending of the light's path depends on the

angle that the incident beam of light makes with the surface, and on the ratio

between the refractive indices of the two media (Snell's law). The refractive

index of many materials (such as glass) varies with the wavelength or color of

the light used, a phenomenon known as dispersion. This causes light of

different colors to be refracted differently and to leave the prism at different

angles, creating an effect similar to a rainbow. This can be used to separate a

beam of white light into its constituent spectrum of colors. Prisms will

generally disperse light over a much larger frequency bandwidth than

diffraction gratings, making them useful for broad-spectrum spectroscopy.

Furthermore, prisms do not suffer from complications arising from

overlapping spectral orders, which all gratings have.

Prisms are sometimes used for the internal reflection at the surfaces

rather than for dispersion. If light inside the prism hits one of the surfaces at a

sufficiently steep angle, total internal reflection occurs and all of the light is

reflected. This makes a prism a useful substitute for a mirror in some

situations.

Light of all wavelengths travels through vacuum at the same velocity, c.

When light enters another medium such as air, water, glass, or plastic, its

velocity will be reduced. The index of refraction of light for a particular

substance is defined as the ratio of the speed of light in vacuum to the speed

of light in that substance, that is:

This ratio also depends on the wavelength of the light. It is more properly

written n(λ).Textbooks often give a single value in tables of indices of

refraction but they specify the wavelength for which the index was measured.

According to Snell's Law, a beam of light that moves from one medium to

another is bent toward or away from the normal according to

where θ1 and θ2 are the angles of the light rays in the two media as

measured from the surface normal.

Assume that you have a prism of apex angle Φ. Assume that the index of

refraction of air is 1. A ray strikes the prism at angle θ1 and is refracted at

angle θ2 . The ray then travels to the other side of the prism and strikes the

second surface at angle θ2' and emerges at angle θ1' . The angle

between the beam that emerges from the prism and the beam that initially

struck the prism is called δ, the angle of deviation. δ will be a minimum when

θ1'= θ1 . At that point θ2 will equal θ2' and both will equal Φ/2. Since the

index of refraction varies with wavelength θ1 and the angle of minimum

deviation will be slightly different for each wavelength but θ2 and θ2' will

always be the same.

You can use Snell's Law to find the index of refraction of the prism if you

know θ1 and θ2 . There is no practical way to measure either angle. However,

you can use simple geometry to express θ1 and θ2 in terms of angles that are

easy to measure, namely δmin and Φ.

You can show that the index of refraction of a prism as a function of the

wavelength, n(λ) , in terms of the apex angle δmin , is and the angle of

minimum deviation

δ can be found experimentally by observing light of known wavelengths

through a prism and varying the angle 1θ . This gives you everything you

need to calculate n(λ). This is not a linear function; a plot of n(λ) vs. λ will

produce a curve.

IV. Procedure of Experiment

This experiment is done by concerning the following steps below.

1. Arrange the equipment as following figure

2. Place the prism on top of HVS paper, then drawing prism suitable shape.

D2

Red

Violet

FLight source

NormalNormal

i

G

D1

E’C

I II F’

B

3. At point C draw a normal line. Normal line is perpendicular to the

surface of the prism refracting I.

4. Attach collimator (light source), set the laser beam coming out of the

collimator in order to obtain light beams that form the angle BC i toward

the normal line.

5. Put a dot with a pencil at points B, C, E, and F.

6. Raise the collimator and the prism, then drawing a line BC, CE, EF (and

E’F’ if in the form of spectrum).

7. Furthermore, the CG line drawing by extending the line BC and line

drawings extension FE (and E'F 'if in the form of spectrum) to cut the

line CG. The intersection of the two second extension of the line is

producing angle D.

8. Measure i and angle D with a protractor and record the results of

measurements on the observation sheet.

9. Repeat steps 2 to 8 of 10 times for obtaining angle i and D.

V. Technique of Data Analysis

The steps of data analysis can be done as follows .

1. Make a graph of relations i and D, with i on the x axis and D on the axis i

and D on the y-axis for the red and purple spectrum

2. Determine the minimum D based on the graph of red and purple spectrum

3. Express the minimum deviation in the form

=

For is the angle of minimum deviation obtained through chart and is

½ nst of the protractor to calculate i and D.

4. Further analysis to calculate the refractive index of prism by using equation

3 for both red and purple spectrum. Since we are here using one value

then the error calculation of refractive index is :

Δn=− 1

sin ( β2 ) (

cosδ+ β

2 )Δδ

so that the prism refractive index of red and purple spectrum are

respectively

n1 = nm nm and n2 = nu nu

While the average refractive index can be searched by the equation

n̄=n1+n2

2

Δn=Δnm+Δnu

2

With relatif error

No Angle i ( 0 )Angle D

Red spectrum ( 0 ) Violet spectrum ( 0 )

1 30 44 46

2 32 42 44

3 34 41 43

4 36 40 42

5 38 37 39

6 40 36 38

7 42 37 39

8 44 36 38

9 46 35 36

10 48 34 36

VI. Result of Experiment

The result of experiment that we get is:

VII. Analysis of Experiment Result

Before starting the analysis let we make the graph about red spectrum and

violet spectrum by the relation about the angle of light source and the prism

refraction index of the red spectrum and violet spectrum. The graph will

explain how much the refraction index of prism by the light souce. The graph

as follows:

Red Spectrum

1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

35

40

45

50

Angle i(0)

Red

Spec

trum

(0)

30 32 34 36 38 40 42 44 46 48

Violet Spectrum

1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

35

40

45

50

Angle i(0)

Viol

et S

pect

rum

(0)

Based on the graph, it can be known that the minimum deviation angle for

red spectrum is 34o and the minimum deviation angle for violet spectrum is

360. This is an acceptable result if we analyzed based on the significance of

minimum deviation angle. In other hand, the minimum deviation angle of the

prism depends to the spectrum. For the spectrum which has the highest

frequency or the shortest wavelength is going to have the largest minimum

deviation angle, inversely. So we can make it to:

a. Red spectrum = (34,0 ± 0,5)0

b. Violet spectrum = (36,0 ± 0,5)0

Then after we know the deviation angle above so we analyze it by:

1. Red Spectrum

Determine Prism refractive index

nr=sin( +β

2)

sin (β2)

nr=sin( 34+60

2)

sin (602)

nr=sin(47)sin (30)

30 32 34 36 38 40 42 44 46 48

nr=0.7313

0.5 = 1.46

Error of the experiment

∆ nr=−1

sin( β2 )

(cos+β2 )∆

∆ nr=−1

sin( 602 )(

cos34+60

2 )0.5

∆ nr=−1

sin (30 )(cos47 )0.5

∆ nr=−1

sin (30 )(cos48.5 )0.5

∆ nr=¿ - 0.68

So, the prism refractive index of red spectrum:

n1= (nr ± ∆ nr )n1= (1.46 ±0.68 )

2. Violet Spectrum

Determine Prism refractive index

nv=sin(+ β

2)

sin (β2)

nv=sin( 36+60

2)

sin (602)

nv=sin(48)sin (30)

nv=0.743

0.5 =1.49

Error of the experiment

∆ nv=−1

sin( β2 )

(cos+β2 )∆

∆ nv=−1

sin( 602 ) (

cos36+60

2 )0.5

∆ nv=−1

sin (30 )(cos 48 ) 0.5

∆ nv=−1

sin (30 )(cos 48 ) 0.5

∆ nv=−¿0.67

So, the prism refractive index of violet spectrum:

n2=(nv ± ∆ nv)n2=(1.49± 0.67 )

3. The average of refraction index (refraction index of the prism):

n=nred+nviolet

2

n=1.46+1.492

n=1.47

4. The error of refraction index of the prism:

∆ n=∆ nred+∆ nviolet

2

∆ n=(0.68 )+(0.67)

2

∆ n=0.67

5. The relative error of refraction index of the prism:

ℜ=∆ nn

x 100 %

ℜ=0.671.47

x 100%

ℜ=45.9 %

VIII. Result and Discussion of Analysis Data

1. Result of analysis data

From the analysis data that we have done we get the value of red

spectrum is n1= (1.46 ±0.68 ) and for the violet spectrum is

n2=(1.49± 0.67 ) .

The average of refraction index is n=(1.47 ± 0.67) with relative error

45,9%.

2. Discussion

Based on these results, it is known that the red light spectrum has a

smaller refractive index than the violet light spectrum. This occurs

because the red light spectrum has greater wavelength than the violet

light spectrum. If the wavelength of a spectrum be larger, so the

refractive index would be smaller. Conversely, if the wavelength of a

spectrum be smaller, so the refractive index would be greater. In

theory, the refractive index of the prism is 1.5, this approach with

experimental results that have been done. However, the results of this

experiment have errors more then 10% so it can not be accepted.

It influenced by many factors, there are:

1) Gross error; largely caused by human error, among them

misreading of instruments, incorrect adjustment, improver

application of instruments and computational mistakes. In this

experiment, we get some error as follows.

a. The accuracy when sketch the prism in the HVS paper.

b. The accuracy when pointed the refractive light.

c. The accuracy when read the scale of protractor.

2) Systematic error divided into two error, such as:

a. Instrumental error; the error caused from the instruments. In

this experiment, there are no errors that came from the

instrument, because there are no mistakes of the instruments.

b. Environmental error; the error caused from the environment.

In this experiment, the environmental error that caused the

error is the sun shine that came from outside of laboratory.

That make we get trouble when pointed the spectrum of the

light (red and violet spectrum), so difficult to see the color of

light spectrum and the outer side of the light spectrum. We

must use the HVS paper to block the sun shine that come

from the outside laboratory.

3) Random error; the error due to unknown causes and occur even

when all systematic errors have been accounted for.

IX. Conclusion

From the experiment and analysis that we have done, we can conclude:

1) The value of red spectrum is n1= (1.46 ±0.68 )

2) The value of violet spectrum is n2=(1.49± 0.67 )

3) The average of refraction index is n=(1.47 ± 0.67) with relative error

45,9%.

4) the relative error is so large because in the experiment we had some

error such as:

a. The accuracy when sketch the prism in the HVS paper.

b. The accuracy when pointed/marked the refractive light.

c. The accuracy when read the scale of protractor (misreading the

protractor scale).

d. The sun shines that come from the outside laboratory.

Reference

Djonoputro, B.D. 1977. Teori Ketidakpastian. Bandung: Universitas ITB.

Giancoli, D. 2001. Fisika edisi kelima jiild I. Jakarta: Erlangga

Halliday, D., Resnick, R., and Walker, J. (1993), Fundamentals of Physics, 4th

edn (extended), John Wiley & Sons, New York.

Suardana, Kade. 2007. Petunjuk praktikum laboratorium fisika 3. Singaraja:

Universitas Pendidikan Ganesha

http://en.wikipedia.org/wiki/Prism_%28optics%29