Refraction of Light by Water

Table 2 – Refraction of Water into Air

Calculations and Analysis

• Sample Calculation of Sin i

Table 1 Observation 5

Formula:  

where i =  40.0°

Sin I     =

        

=

        

=0.643 ± 0.027

        

• Sample Calculation of Sin R

Table 2 Observation 3

Formula:  

where i =  20.0°

Sin R   =

        

=

        

=0.485 ± 0.031

• Sample Calculation of Sin i/SinR

Table 1 Observation 8

Formula:  

where x=Sin i

         ∆x=Uncertainty of Sin i

           y=Sin R

         ∆y=Uncertainty of Sin R

Sin r         =

        

=1.22 ± 0.03

• Sample Calculation of Slope of Refraction of Light by Water

Formula:  

                where a=sin i

                           b=sin R

                           c=slope

Slope        =  

        = 1.10

• Testing Snell’s Law

Table 1 Observation 7

Formula: n1sinθ1=n2sinθ2

                where n1=1.0003 (air)

                           sinθ1=0.866

                           n2=1.33 (water)

                           sinθ2=0.707

           

           1.0003 * 0.866 = 1.33 * 0.707

           1  1.08

           

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QUESTIONS:

Refraction of Light by water - p.46

1. When light travels from air into water with an angle of incidence of 0° along the normal, light goes straight through the medium with no apparent “bending” (i.e.: refracted ray is at 0° of the normal)

2. When light travels from air to water at an angle of incidence greater than 0°, light is “bent” towards the normal because water is a denser medium than air.

3. During my experiment, the incident ray and the refracted rays were always on opposite sides (i.e.: incident rays always stayed on the right side of the normal and the refracted rays stayed on the left).

4. The angle of refracted ray is always smaller than the incident ray in each case.

5. Any sin i/sin R ratio greater than 0° are all relatively similar and close to the theoretical index of refraction of water (n=1.33)

6. If light travels from water into air, it will be “bent” away from the normal.

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Refraction of water by Light – p.47

1. There was no refraction when the angle of incidence was 0°

2. When light travels from water to air at an angle other than 0°, it is “bent” away from the normal.

3. The angle of refraction is always higher in each case.

4. The incident and refracted rays are located on either side of the normal (i.e.: incident rays always stayed on the right side of the normal and the refracted rays stayed on the left).

5. The sini/sinR ratio after 0° are mostly similar except for angles greater than 50°

6. There is an inverse relationship between the index of refraction of water and air (1.33 and 0.75 respectively). Because the index of refraction in water is higher than that of air, when air (n=1) travels through water, it is “bent” away from the normal but when that same ray travels back from water into air, the second refracted ray is parallel to the original incident ray. Using Snell’s Law and the data from “Table 1 Observation 4” and “Table 2 Observation 3” shown below, we can see the relationship clearly.

When,        Incident ray into water = 30.0°, Sin i/Sin R=1.46

Refracted ray out of water = 20.0°,

After,         Incident ray from water = 20.0°,

        Refracted ray back out of water = 29.0°, Sin i/Sin R=0.705

The angles of original incidence and final refraction are the same, thus the angles of the light are parallel. In addition, when we multiply the two sin ratios together we get approximately the index of refraction of air (n=1), which is the medium in which both the initial and final rays move through (i.e.: 1 * 1.46 * 0.705  1).

7. As the incident angle increases, more of the incident light is reflected from the medium.

8. Above 50.0° at the boundary between water and the air, all the light is reflected.

9. At the critical angle 50.0°, the angle of refraction is 90.0° according to “Table 2 Observation 6”.

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SOURCES OF UNCERTAINTY:

• Impurities in water and air will have caused the light to be refracted more than the expected theoretical values. As well, the index of refraction (n) for the two substances would be inaccurate.
• The plastic dish holding the water may have will have slightly refracted the light.
• Light from the ray box is completely focused and coherent, thus readings may be inaccurate.

CONCLUSION:

Light is refracted towards the normal when it passes from air into water and away from the normal when it passes from water into air because of a change in the medium’s density. The index of refraction of water (n=1.33) can be found by dividing the sin of the incident angle by the sin of the resulting refractive angle as shown in my sin i/sin R calculations. And if we reflect light by water and back into air again, the light will travel in the same direction as the original incident ray due to the inverse relationship of the indices of refraction as shown in my analysis.