Reflection and Refraction

Here’s to my very first blog post.. ever.

“Who is that girl I see staring straight back at me? Why is my reflection someone I don’t know?”

When a light wave strikes a smooth surface separating two different materials, the wave is reflected and refracted. The common denominator? Both is a change in the direction of the propagation of the wave. The difference? Reflection is bouncing, the abrupt change when wave strikes the boundary between two media. Refraction is bending, the change in speed of light as it passes from one medium to another.

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Figure 1. Reflection and refraction of light at the interface of two different media n1 and n2

For the experiment, the alignment of optics was done as if you were calibrating. Just align the light source, parallel ray lens, slit plate, slit mask (for a single ray), and the optical disk, with the grid facing up, all on the optical bench then adjust the ray to coincide with the 0°-0° axis of the optical disk. And we’re all set.

 The first part of the experiment aimed to test the law of reflection stating that the angle of incidence Ѳi is equal to the angle of reflection Ѳr.

                                                                Ѳ= Ѳi                                                                       (1)

Table 1. Reflection by plane and spherical mirrors

Table 1

With the optics aligned, the angles of reflection of plane mirror above the optical disk was determined at different angles of incidence. Same goes with the concave and convex mirrors. From table 1, it could be said that the law of reflection applies to the mirrors used for this setup. However, this is just an approximation since the optical disk used has a ±0.5° deviation.

The goal of the second part of the experiment is to trace the path of light ray for plane and spherical mirrors.

Figure 2.1. (left) plane mirror, (middle) convex mirror, and (right) concave mirror

  1. In a plane mirror, incident rays and reflected rays are parallel
  2. In a convex mirror, the reflected light rays are diverging
  3. In a concave mirror, the reflected light rays are converging

 

Figure 1

Figure 2.2. Ray tracing for plane, convex and concave mirrors

The objective of the third part is to measure the index of refraction of a material using two setups for a semicircular (cylindrical lens) glass with the alignment of optics. The index of refraction n is the ratio of the speed of light c (3 x 108 m/s) and the speed of light v in the medium

                                                                                  n = c/v                                                                       (2)

Moreover, the index of refraction of a medium can also be calculated with the help of the law of refraction, also known as Snell’s law, stating that the ratio of sines of the angles of incidence Ѳi  and refraction Ѳt is equal to the ratio of the index of refraction of the incident medium nand the index of refraction of the transmitting medium n

                                                                           ni sin Ѳi = nsin Ѳt                                                                       (3)

figure 2

Figure 3. (a) light propagation on the flat surface, (b) light propagation on the curved surface

Setup a shows the reflection and refraction of light on the flat surface of the cylindrical lens while setup b shows the reflection and refraction of light on the curved surface of the semicircular glass. The angle of incidence was varied from 10° to 50° with increments of 10°.

Table 2.1. Reflection and refraction of light with the incident ray striking the flat surface

w2.

The first setup with the incident ray striking the flat surface has air as the transmitting medium and the glass as the incident medium. To compute for the index of refraction of glass, (3) was used with the nas the index of refraction of air (1.0003). Table 2.1 showed the indexes of refraction of the setup for different angles of incidence. It could be seen that the angles of reflection and refraction are following an arithmetic trend. Going back to (1), we can see that the angles of incidence are not equal to the angles of reflection.

Table 2.2. Reflection and refraction of light with the incident ray striking the curved surface

w3

The second setup with the incident ray striking the curved surface has air as the incident medium and glass as the transmitting medium. To calculate the index of refraction of the glass, (3) was again used but with the index of refraction of air as ni. From the table, the indexes of refraction of glass were shown. Using the angles of refraction from table 2.1 as the angle of refraction for this setup will obtain a different result since the media for incident and transmitting are not the same.

Errors that may ave propagated are (1) the parallel ray lens is not clear enough, (2) the semicircular glass is not is the center of the optical disk, and (3) the semicircular glass may have components other than glass such as impurities. Moreover, the indexes of refraction calculated for this part of the experiment are considered precise and accurate since the values are at the range of 1.52 to 1.80 for different types of glasses.

At 50°, the angle of refraction says TIR, which stands for Total Internal Refraction, a phenomenon when the a the angle of incidence is larger than the critical angle Ѳc, the angle of incidence for which the refracted ray emerges tangent to the surface. The sine of the critical angle for the total internal refraction is equal to the ratio of the indexes of refraction of the incident medium (larger) and the transmitting medium (smaller).

                                                            sin Ѳc=n / ni                                                                                                        (4)

This leads to the fourth part of the experiment where the critical angle was determined by adjusting the optical disk until the refracted ray is parallel to the flat surface.

figure 4

Figure 4. (left) refracted ray is parallel to flat surface (right) no more refracted ray

The left part of the figure shows when critical angle is equal to angle of incidence. The right part shows total internal refraction where critical angle is smaller than the angle of incidence.

Table 3. Total internal reflection

s4

The critical angle for the total internal reflection is found to be 41°. The index of refraction of glass was calculated using (4) with air as the transmitting medium. The speed of light, on the other hand, was computed using (1) with the index of refraction equal to 1.52.

For the last part of the experiment, the path of light was traced as it emerged from different refracting media.

Figure 5.1. (upper left) right triangular lens (middle) triangular lens (upper right) trapezoidal lens (lower left) double convex lens (lower right) double concave lens

Here’s a sketch I tried to make using MS Paint of the ray tracing of the different refracting media.

Figure 3

Figure 5.2. Ray tracing for different refracting media (a) right triangular lens (b) triangular lens (c) trapezoidal lens (d) double convex lens (e)

Finishing my first blog post after hours, with the interesting optics as the topic, is a milestone in my life.

” The law of reflection is not true at all times. Try looking at a different angle, you’ll see the closest “you” that you know.”

References:

[1] Young, Hugh, and Roger Freedman. University Physics with Modern Physics 13th edition. Pearson Education Inc, 2004.

[2] “Reflection and Refraction.” N.p., n.d. Web. 7 Feb. 2016. <http://electron9.phys.utk.edu/optics421/modules/m1/reflection_and_refraction.htm&gt;.

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One thought on “Reflection and Refraction

  1. Hi iel!

    Neat presentation! I like the added drama while telling the ‘story’ of your experiment. Next time, explicitly state all the objectives of the study.

    Overall, the report is complete! Excellent start! 😀

    Liked by 1 person

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