# Aim To determine the refractive index of a material and the speed of light in order to calculate the expected critical angle at which total internal reflection occurs

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Introduction

Practical Experiment 3:

Refraction and Reflection of Light

Aim

To determine the refractive index of a material and the speed of light in order to calculate the expected critical angle at which total internal reflection occurs.

Hypothesis

As the sin of the angle of incidence increase, the sin of the angle of refraction also increases

Theory

There is a strong relationship between the angle of incidence and angle of refraction of lights. Light can pass through different materials, assuming that it is transparent. It can also pass through two different isotropic materials such as air to glass. When light passes from one isotropic material with a high refraction index to another isotropic material with a lower refraction index, there is an angle where light passing through gets reflected and refracted (Young 2011). Snell brought up a law, which determines the angle at which light bends according to the initial angle and also the refraction index of materials. Where he derived the formula;

where

= refractive index of material a

= refractive index of material b

= sin of angle of incidence

= sin of angle of refraction

(Young 2011)

Middle

0.485°

0.559°

0.602

0.629°

Table 1.1 Resolution: Protractor = 1°

Graph of the Sin of the Angle of Incidence and Angle of Refraction

Graph 1.1

From Snell’s law, the gradient (1.55) of the graph is =

;

Hence to determine the refractive index of the semi-circular prism protractor, Snell’s law formula must be use

given that

is the refractive index of air, which is 1.000293, and

x

x 1.000293

Hence the refractive index of the prism is 1.55

Calculating the speed of light within the semi-circular prism protractor

Given that

where n = refractive index of the semi-circular prism protractor (1.55)

c = the speed of light in a vacuum (2.99792458 x 108 ms-1)

v = speed of light in the semi-circular prism protractor

1.93 x 108 ms-1

1.93 x 108 ms-1

Calculating Uncertainties

Uncertainties for angle of incidence = 0 as it is the Independent variabl,e a set value not a measurement

Uncertainties the angle of refraction (b) is

=

=

Therefore the uncertainties for sina is ± 14.0

, hence;

Angle of Refraction (b° | 0 ± 14.0 | 6± 14.0 | 12± 14.0 | 19± 14.0 | 25± 14.0 | 29± 14.0 | 34± 14.0 | 37± 14.0 | 39± 14.0 |

Hence, the uncertainties for the sin of the angle of refraction is sin (±14.0) = ±0.242

Sin b° | 0± 0.242 | 0.105± 0.242 | 0.208± 0.242 | 0.326± 0.242 | 0.423± 0.242 | 0.485± 0.242 | 0.559± 0.242 | 0.602± 0.242 | 0.629± 0.242 |

Thus, the uncertainties for the refractive index = ±0.263

1.55 ±0.263

Hence the refractive index can be between 1.287 and 1.813 (when considering the uncertainties)

Conclusion

(example: 27

and

). By not being able to determine exactly where light was refracted, this affects the slope of the graph and its accuracy, hence affecting the value for the refractive index, which also leads the value for the speed of light in the glass and the total internal reflection.

A possible improvement to this is to use a light with higher intensity. This will make the ray stronger and the degree of refraction would be easier to distinguish.

Conclusion

The refractive index of the material, semi-circular prism protractor was determined to be 1.55, which is a clown glass, from the use of the gradient of the graph of

. The refractive index also gives rise to the speed of light in that clown glass at 1.93 x 108 ms-1, and at which angle the light will have a total internal reflection, which was determined to be at

. Though there were uncertainties calculated for the angle of refraction, which gave rise to errors, which may have occurred in the practical. Nevertheless an improvement was suggested. Overall the hypothesis was supported by the results obtained by conducting the practical.

Reference

Young, HD 2011, College Physics, 9th edn, Addison-Wesley, Boston, US

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