Experiment 9: Reflection, Refraction, and Total Internal Reflection

Purpose:
The purpose of this experiment was to study the laws of reflection, refraction and total internal reflection, to measure the focal length of mirrors with convex and concave mirrors, and to measure the index of refraction of water.
Theory:
In this experiment, we learned that the angle of incidence θi is the angle that the incident ray makes in regards to the normal one. Also, the angle of reflection θr is the angle that the reflected ray produces from the normal one. Also, we discussed how the law of reflection is used to explain the behavior of the incident and reflected rays. According to Snell’s law, we observed that the incident ray, the reflected ray, and the normal line to the surface, all lie in the same plane and θi=θr.

During the experiment we analyzed, the light striking the interface between two transparent materials and part of the light was reflected. The angle of the reflection equaled to the angle of incidence. The rest was passed along the interface and the ray entered that entered the second material was refracted. When light travels from medium #1, with a refractive index being n1, into the medium #2, with refractive index n2, the equation sinθ1= n2sinθ2.

Lastly, we did a test that shows that when a light passes from a medium of large refractive index into one of small refractive index, the refracted ray it produces bends away from the normal because of the equation: n1>n2⇒sinθ1<sinθ2⇒ θ1<θ2 . Therefore, as the angle of incidence goes up, the angle of refraction also goes up. When the angle of incidence reaches a certain value, called the critical angle θc, the angle of refraction is 90°. When the angle of incidence is more than the critical angle there is no refracted light. An important concept that we got from this is that all of incident light is reflected back into the medium from which it came. This is known as total internal reflection. Total internal reflection occurs only when the light travels from higher-index medium toward lower-index medium. sinθc=n2sin90°n1=n2n1 with n1>n2

Procedure:
First, We used a ray box as a light source and adjusted the number of white rays by maneuvering a plastic piece that allows 1, 3, or 5 rays to show. We needed to turn on the power for the light source, turn off the lights in the room and position a sheet of paper with certain types of mirrors so that the light rays could strike the mirror at different angles.

EXPERIMENT 9.1:
Reflection
* Adjust the slit mask on the light source so one ray shines to the surface of the triangular mirror. * Rotate the mirror * Trace the surface of the mirror and mark points on the incident ray and the reflected ray * Trace the incident ray and reflected ray in three different angles. * Repeat these steps with the concave and convex mirror surfaces facing the light source. Table 1 Plane surface | Concave surface | Convex surface | Incident θi | Reflected θr | Incident θi | Reflected θr | Incident θi | Reflected θr | 90 | 67 | 90 | 68 | 90 | 65 | 90 | 67 | 90 | 68 | 90 | 65 |

EXPERIMENT 9.2:
Focal length of the Mirror * Adjust the slit mask on the light source until three parallel light rays are shining. * Place the concave surface facing the light source. * Adjust the mirror so that the middle reflected ray is aligned with the middle incident ray.
The place where the three reflected rays cross each other is the focal point of the mirror. * Trace the concave mirror surface and three reflected rays. * Measure the focal length f from the middle point on the surface to the focal point and compare it with the radius R of the curvature of the mirror. * Use the compass to draw a circle that matches the curvature of the mirror * Check that f = R/2 * Repeat this procedure with the convex mirror surface and note that the reflected rays are diverging and they will not cross in front of the mirror. * Use a ruler to extent the reflected rays back behind the mirror’s surface to find the focal point.

EXPERIMENT 9.3:
Refraction of light passing from air through water
A refraction tank consists of a circular bath, which has a built-in scale and light source. * Measure the angles of incident, reflection and refraction on the scale.
The water is filled up to the line of 90°-90° in the tank. The incident point of the light is at the center of the tank. * Slowly move the light source from its top position (zero on the scale) * Record the angles and calculate the refractive index of water nwater by Snell’s law nairsinθair= nwatersinθwater ⇒ nwater=sinθairsinθwater Angle of incidence θair | Angle of refracted θwater | nwater | Average of nwater | 50 | 35 | 1.33 | 1.33 | 30 | 22.15 | 1.30 | | 15 | 11 | 1.36 | |

EXPERIMENT 9.4:
Refraction of light passing from water into air

1. Record the angle of incidence θwater and the angle of refraction θair and then calculate the refractive index of water nwater by Snell’s law nairsinθair= nwatersinθwater ⇒ nwater=sinθairsinθwater Angle of incidence θwater | Angle of refraction θair | nwater | 40 | 57 | 1.30 |

2. Set the angle of refraction 90°, the angle of incidence reaches the critical angle θc. Calculate the refractive index of water nwater. Angle of incidence θwater=θc | Angle of refraction θair | nwater | 52 | 90° | 1.27 |

3. Set the angle of incidence larger than critical angle as shown in figure above. All of incident light is reflected back into the water, total internal reflection occurs.

Angle of incidence θi | Angle of refraction θr | 61 | 57 |

Questions and Exercises: 1. Under what conditions the laser beam can travel through fiber optic cable Demonstration (3)? * Due to the fact that it was a total internal reflection demonstration, light should travel from a high index medium to a lower one. Also, the angle of incident should be greater than critical angle. The cable shouldn’t have any holes in it, otherwise it won’t work. 2. Does total internal reflection occur if the refraction of light is passing from air into water? * No it does not occur because the light should go from a denser to rare medium. 3. List the methods that can be used to determine the index (nglass) of refraction of a glass. * According to Snell’s law, if n is the refraction index of the material that is to be determined, i is the angle of incidence, and r is the angle of refraction, then nairsini=n2sinr. We can determine n=sinisinr because if we know the angle of incidence and the angle of refraction going into the material, we can determine the refractive index of the material.

4. Explain how the rainbows are formed? * After it rains, water droplets are left floating in the air. As sunlight passes through these spherical-shaped droplets, light is bent and scattered into a continuous band of colors. This light is reflected off the back of the drop and refracted again as it leaves the drop.

5. Figure 12 shows an optical fiber that consists of a core made of flint glass (nflint=1.667) surrounded by a cladding made of crown glass (ncrown=1.523). A beam of light enters the fiber from air at an angle θ1 with respect to the surface normal. What is θ1 if the light strikes the core-cladding interface at the critical angle? * θc=sin-1(n2n1= 1.5231.667)⇒θc=66.01° * θ2=90°-66.01°=23.99° * ⇒ θ1=sin-11.667*sin23.991.00=42.67°

Conclusion:
In this experiment, we studied the laws of reflection and have observed how the angle of incident is equal to the angle of reflection. Also, we noticed that all of the rays are on the plane of incidence. In addition, we discussed the Refraction law described by Snell’s law of refraction. Thus, the total internal reflection is when the incident angle is larger than critical angle. We have measured the focal length of mirrors with convex and concave surfaces and we observed that the focal length is half of the radius of curvature of the mirror’s surface. We concluded this by drawing a circle with a diameter that related to the radius. Lastly, we understood that Snell’s law of refraction is a useful tool for determining and measuring the index of refraction of water as well as the other optical media that are similar in transparency.