INDEX OF REFRACTION Pineda, Ram Lewis N, PHY13L/A2 ramlewis2!"mail#$%m
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This paper was written to further understand the concept of refraction – quantitatively. The study was conducted using a glass plate and air as the medium of light propagation. Both media were interchanged to establish a consistent relationship with the said topic. It was found out that that the value of the index of refraction is always greater than 1. The obtained data shows that the greater the value of the index of refraction of certain medium, the denser is the medium. This was verified by using the nell!s "aw, in which the experimental index of refraction was determined accordingly. #oreover, it is also found out that when a light ray travels in medium with considerable refractive index into much lesser refractive index a total internal reflection occurs between the interfaces of media. The results of this experiment were very promising in understanding the concept of refraction.
(e) *%rds+ light, refraction, index of refraction, critical angle, Snell’s Snell’s Law
In'r%d$'i%n
$. "ight has a dual nature ometimes ometimes it behaves li%e a particle &called &called a photon', photon', which explains how light travels in straight lines ometimes it behaves li%e a wave, which explains how light bends around an ob(ect. If light would be considered as a wave, it entails the principles of propagation and other properties of wave. These principles can be narrow down in the concept of reflection and refraction. refraction. )eflection is the change in direction of a wave front at an interface between two different media so that the wave front returns into the medium from which it originated. *n originated. *n the other hand, refraction is the change in direction of a wave passing from one medium to another caused by its change in speed. If a light ray travels and it is propagated in a certain medium it will travel in a constant density. +owever, if light travels in certain number of medium &media', at least of two medium, it is observed that light travels in different speed depending on the very structure of the material or the medium. The very reason of this refraction of light is that a change in speed of light ta%es place in the interface between the media. $s a result of study, different media have different quantitative value of refraction. These quantitative values are often refereed as the index of refraction.
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In this fourth experiment, it will be divided into three parts.&$' etermination of index of refraction of glass when light goes from glass into air, &B' etermination of index of refraction of glass when light bends from air into glass, and &-' etermination of the critical angle for glass. To perform the experiment about the index of refraction the following materials are needed glass plate, push pins, cor% board, and either diode laser or a laser pointer.
3igure 1. The materials used in the experiment The first part is about the determination of index of refraction of glass when light goes from glass to air. o this part will be done on the data sheet containing two perpendicular axes and the circle. *n the datasheet with the drawing of two perpendicular axes $$! and BB! intersecting at the center of circle *, the glass plate!s lower edge must be placed along the line $$!. Then, trace the exact si/e of the glass plate. 0ext, is to put a pin on the point * &origin' and pin anywhere on the first quadrant and label it as point T. It is important that the two pins must touch the sides of the glass plate. 0ext thing to do is to view the thic%ness of the lower edge of the glass plate and loo% for the images of pin 1 and pin . These two pins must be aligned and place the third pin anywhere in quadrant III in alignment with the pin 1 and pin . )emove the glass plate and identify the hole from the pin on the paper, after doing so, draw an extended line connecting points * and T to intersect the circle at + and another extended line connecting points * and 2 to intersect the circle at 3. Then the angle must be determine using a protractor or can be calculated using the analysis of the right triangle formed by pro(ecting the intersection of both extended line at the circle in the hori/ontal and vertical axis. $ll data must be recorded.
3igure et5up for the first part of the experiment
The second part of the experiment is most li%ely the same with the first part of the experiment. It simply means that the procedure son in the first part is the same for the second part. The only difference is that the glass is place below the hori/ontal axis, thus the upper edge of the glass plate is actually touching the hori/ontal axis. till, one must view in the thic%ness of the glass plate in the third quadrant loo%ing for the image of the second push pin. $ll places where the push pins are found out to be located must be traced from the center. $gain, the angle can be measured using a protractor or can be calculated as well. $ll data must be recorded.
3igure 4 et5up for the second part of the experiment In the determination of the critical angle, which is the last part of the experiment, the first thing to do is to place and trace the glass plate in a clean sheet of bond paper. Then, a laser must be placed to the lower side of the glass plate. The laser must be somehow perpendicular to the glass plate this can be done by ad(usting the laser until the incident ray of light appears to be almost parallel to the lower side of the glass plate. $ light ray will be observed emerging in the upper side of the glass plate, the position of both laser and the 4
emerging light ray must be mar%ed. $gain any letter will do to assign these points. In the case of our data, the position of the laser is set to be letter # and the point of the emerging light ray at the upper side of the glass plate was assigned to be letter 6. $ line must be trace from point # up to point 6. The angle of this trace line must be measure with respect to the vertical axis7 also it can be calculate by using the tangent function. $ll data must be recorded. ee figure 8.
3igure 8 et5up for the last part of the experiment, the diode laser is pointed out at the lower end of the glass plate
Resl's and Dis$ssi%n
The conducted experiment about index of refraction is relatively easy. The following data and relationship established are provided below. $. etermination of index of refraction of glass when light goes from glass into air If you would ta%e a loo% in figure 9a, it is noticeable that the angle in the first quadrant in much lesser than the angle in the third quadrant. It is important to note that all these angles are with respect to the vertical axis. The very explanation of this findings is that light bends lesser in much denser material provided that its molecules is more compact than a less denser material that its molecules are less compact. olids are the best example of material which have a compact molecules, while gas are the best example of materials which a less compact or scattered molecules. In the experiment, the glass plate which is placed in the upper part of the hori/ontal axis, which is also solid in nature, which is the push pin was initially place, served as the basis for where the push pin 4 to be placed. Theoretically, the angle with respect to vertical axis of the third push pin is expected to be more than the angle produce of the initially place push pin due to the above explanation given. In the case of our data, the theory was not violated since the angle of the third push pin is greater than the angle of the second push pin, again with respect to the vertical axis. :e were able to determine the angle
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by using a protractor for accuracy reason, but this angle was also calculated using the principle of right triangle. B.
etermination of index of refraction of glass when light bends from air into glass
Basically, the same principle is observed in the second part of the experiment. $gain push pin was initially place in the first quadrant, and we are tas%ed to determine the angle of refraction in the third quadrant, specifically to locate where the image formed in the third quadrant by loo%ing at the thic%ness of the glass. $s explained above, less angle, much denser material7 higher angle, less denser material. This theory is still observed in data obtained in the second part of the experiment. ince the glass plate was placed below the hori/ontal axis, ma%ing the angle of refraction of push pin , in which the push pin 4 was placed, much lesser than the initial angle produced of push pin in the first quadrant. ee figure 9b. &a'
&b'
3igure 9. &a' $ctual data obtained in the frist part of the experiment, &b' $ctual data obtained in the second part of the experiment
;enerally, all findings and relationship established in the first and second part of the experiment is governed by the nell!s law. $lso, the formula used in determining the experimental value of the index of refraction of the glass was derived from the equation of nell!s law.
where,
is the index of refraction of glass7
angle of incidence7 and
is the index of refraction of air7
is the
is the angle of refraction &$ll argument are in degrees'
Table 1 Determination of index of refraction of glass PART A
PART
"ight bends from ;"$ to $I)
"ight bends from $I) to ;"$
"ength of line ;+ 9
"ength of line 3" Index of )efraction of $ir Index of )efraction of ;lass
&6xperimental =alue' Index of )efraction of ;lass
&$ccepted =alue'
-.
etermination of the critical angle for glass
In the table provided it is observed that the percentage of error is most li%ely close to ten percent, but the percentage of error obtained in this part of the experiment is reasonable due to the structure of the glass plate. It observed the glass plate is not perfect rectangle as a result it highly affects the data obtained, since the concept of critical angle is highly dependent on the angle how the laser is pointed into the glass plate. +owever, we are still able to gather reasonable data to emphasi/e the concept of critical angle. The very reason why the critical angle exists is because a total internal reflection occurs. This means there is no refracted ray but the ray of light is totally refracted. :ith some extended research, there are two requirements in order for a total internal reflection can occurred, first is that the light is in the more dense medium and going to less dense medium, and second the angle of incidence must be greater than the critical angle. The concept of the critical angle is still governed by nell!s law. Table etermination of critical angle "ength of line #> "ength of line 6> -ritical $ngle &6xperimental =alue' -ritical $ngle &$ccepted =alue'
C%n$lsi%n
There are three ob(ectives in this experiment &1' to study the refraction of light, &' to compare the angle of incidence in the first medium to the angle of refraction in second medium, and &4' to determine the index of refraction of glass experimentally by applying the nell!s "aw. The first and second ob(ective of this experiment was accomplished both in the process of performing the experiment and after the data obtained. In the process of performing the experiment we were able to study the refraction of light on how it behaves in different media7 li%e in the experiment the glass and air used as the medium. $fter the data was obtained we were able to compare the angle produce of the push pin. :e found out that the medium truly affect the angle of refraction. :e were able to establish a relationship that is provided in the results and discussion, between the angle and the medium where the light bends. #oreover, the third ob(ective was accomplished by analysing our data obtained. To ?
determine the experimental index of refraction of the glass we use the nell!s law. There is no ma(or problem encountered in calculating the experimental index of refraction, since nell!s law is very consistent. In addition to the stated ob(ective, we also study the principle of the critical angle that is also can be explained mathematically by the nell!s law. 3urthermore, it is advisable to some extended research to fully understand the concept of refraction. This paper can only support the existing theories ad principle about the said topic. If innovations were introduced, it is advisable to integrate it to the existing experiment in the purpose of further understanding. Re0eren$es
Boo%s @1A erway, ). $., =uille, -., 6ssentials of -ollege
)" @1A httpFFwww.physicsclassroom.comFclassFrefrnF"esson5Fnell5s5"aw @A httpFFhyperphysics.phy5astr.gsu.eduFhbaseFtablesFindrf.html
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