Note: see diagram below for details

Results

Relationship Between Angle of Incidence and Angle of Refraction

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;

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

Hence, the speed of light in the semi-circular prism protractor with respect to the uncertainties can be between

1.65 x 108ms-1 and 2.33 x 108ms-1

Calculating the Critical Angle for the Total Internal Reflection

To determine the angle of total internal reflection, the formula below is to be used;

sin

where, sin

= sin of the angle of total reflection

= Refractive index of the less dense medium (Air = 1.000293)

= Refractive index of the more dense medium (1.55)

hence,

Setup to measure the critical angle

Using the light box, shine the light ray at the prism at

directly as shown in the diagram below

Note: The light will pass through the prism then exit to the air

By performing the experiment, it was found that there was a total internal reflection when the light ray shined at the prism at approximately

Discussion

From following the method, the refraction and total reflection of light was presented through the movement of the semicircular prism protractor. It was found that the refractive index of that material is 1.55 and according to Young (2011) it is a crown glass. The refractive index was determined by using the slope of the graph 1.1 and the known air refractive index. It can be seen from graph 1.1 that there is a proportional relationship between sin of the angle of incidence (

and the sin of the angle of refraction (

, where as

increases,

also increases. This supported the hypothesis made, in which Snell also clarified that the gradient of the graph of

is a constant and the same constant as the gradient of the graph of

, given

. Also the gradient of the graph can also be represent as

, which is the same as

.

Furthermore, by determining the refractive index of the prism, the speed of light in that prism was also calculated to be 1.93 x 108 ms-1. This is slower than the speed of light in a vacuum of

, but that is due to the dense of the material, where the clown glass prism had a higher refractive index (1.55) than the refractive index of a vacuum (1.00).

Also, another experiment was conducted to determine at which angle the light ray shines directly glass prism would produce a critical angle of the total internal reflection. It was found to be approximately 42

, but from calculation, it was found that by using the refractive index of 1.55 and refractive index of air, a total internal reflection should occur at 40.2

.

Though the experiment went exactly according to the method, there are uncertainties within the values of the measurements. Standard deviation was used to determine the uncertainties of the angle of refraction. It was found to be ± 14.0

. Which is approximately ±0.242 for the sin of the angle of refraction. The uncertainties were not calculated for the angle of incidence, as it is a set value, an independent value, which was not measured.

The uncertainties gives rise to possible errors which may have occurred in the practical and one of the error is the difficulty in determining specifically where light was refracted off the glass prism. At times the light ray was thick in which it lies between 3

(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