Lab 4-Reflection and Refraction of Light PDF

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This the Lab#4 formal lab report which is Reflection and Refraction of Light...

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Prof. Williams 2.24.2020

Reflection and Refraction of Light Purpose: The purpose of this experiment was demonstrating reflection and refraction of light. With completing this experiment, we were able to see the law of reflection and also visualize Snell’s law for refraction of light. Reflection and refraction are two of the most commonly properties of light. Equipment list: Pins, Sheet of carboard, Ruler and protractor, Rectangular flat mirror and block, Thick glass plate, Sheets of white paper Procedure: Refraction: 1. First, we drew a line MN across the middle of a plane sheet of paper. Then we put the paper on a carboard and fixed it on the carboard with pins. Then a flat mirror was placed vertically on the drawn line, where the edges of the mirror coincided with MN line, and was supported with wooden blocks. Then one pin was placed vertically at the distance about 7 cm in front of the reflecting side of the mirror. Then we randomly placed two other pins vertically at the points D and E. We normal line form those pins to the line MN and named the intersected pints O and O`. We rotated the board, so we reached a point that the image of original pin P was exactly on the image of placed pin at point D. Then we drew a line along the ruler from the point (point A) that this image was seen. The angle of AOD must be greater than 30o. We have done the same procedure for the placed pin (point E) at other side of the object and drew a line from point B so the line intersected with the mirror. We continued the sight lines and named their intersects point P`. This point is the image position of the object P in the mirror. Figure 1 M A

D

O P'

P

E

O`

B N

2. For the second part of refraction experiment, we placed a pin horizontally in front of the mirror. We have repeated the same procedure as the previous step, however the sight lines has to be drawn two times. First set of sight lines was for the tip of the object, and the second set of sight lines was for the tail of the object. We drew 4 sight lines, so they intersected with the MN line. We continued the sight lines for the tip and tale and named their intersects Tail and Tip. Then we measured the image position and size.

3. First, we drew a line across the middle of a plane sheet of paper and placed a flat mirror on the drawn line. Then we placed the second flat mirror in a position so the edges of two mirrors were at the right angle. Then we placed a pin between two mirrors and recorded the number of seen objects. We also marked the approximated position of the images as points on the paper and behind the mirrors.

Figure 2

90 o Object

4. On this part, we have repeated the same procedure as part 3. However, we placed the mirrors at angles of 60o and 120o and recorded the number of images and marked the image locations on the paper. We have changed the position of the object to see how many images can be seen each time. Refraction: 1. On this part of the experiment, the thick glass plate was placed at the center of a sheet of paper. We drew the outline shape of the plate on the paper. We placed two pins at points A and B next to the two opposite sides of the glass. Then we placed a third pin, C, within the distance of 7 cm from point B such that are three pins were aligned with each other. Then we draw a normal line to the glass plat at the position of the pin B in order to measure incident and refracted angles. We have repeated this procedure with moving the position of the pins to obtain two other sets of incident angles.

Figure 3 C 

Glass plate

B 



A

Data Reflection: 1. Incident angle from point A: 32o Reflected angle from point A: 30o Incident angle from point B: 34o Reflected angle from point B: 29o Distance of P from the surface of the mirror: 7.7 cm Distance of P` from the surface of the mirror: 6.9 cm 2. Object position: 7.7 cm from the front side of the mirror and parallel to the mirror. Image position: 7.7 cm from the back side of the mirror and parallel to the mirror. Object size: 5.4 cm Image size: 5.0 cm 3. Number of images for the mirrors at 90 o : 3 images 4. Number of images for the mirrors at 60 o : 6 images (two images were at the same location) → 5 images Number of images for the mirrors at 120 o : 2 images Sample Calculations: A. Reflection 1. Measure the incident and reflected angles for all of the single plane mirror conditions. Part 1. e(%)= |AE|/A * 100

Percent Errors for angles at A: e(%)= (32-30)/32 *100=6.7% Percent Errors for angles at B: e(%)= (34-29)/34 *100=14.7% Percent Error for object and image distance: e(%)=|7.7-6.9|/7.7 * 100= 10.40% Part 2. Incident angle from point A for Tip: 43o → e(%)=6.97% Reflected angle from point A for Tip: 46o Incident angle from point B for Tip: 37o Reflected angle from point B for Tip: 35o

→ e(%)=5.40%

Incident angle from point A for Tail: 32o Reflected angle from point A for Tail: 32o Incident angle from point B for Tail: 47o Reflected angle from point B for Tail: 47o Percent Error for object and image size: e(%)=(5.4-5)/5.4 * 100=7.40%

2. Determine the relationship between the incident and reflected angles. 𝜃𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 = 𝜃𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 3. Determine the relationship between the object size and distance to that of the image. 𝐼𝑚𝑎𝑔𝑒 𝑠𝑖𝑧𝑒 = 𝑂𝑏𝑗𝑒𝑐𝑡 𝑠𝑖𝑧𝑒 𝐼𝑚𝑎𝑔𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑂𝑏𝑗𝑒𝑐𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 B. Refraction 1. Determine the incident and refracted angles for the three positions of the pins.

Position 1

Incident Angle o 29

Refracted Angle o 48

Position 2

32

55

Position 3

28

45

2. Determine the index of refraction for the glass. Snell’s Law of Refraction: 𝑛 𝑠𝑖𝑛𝜃 = 𝑛 𝑠𝑖𝑛𝜃 𝑛 = 𝑎𝑖𝑟 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 = 1 𝜃 = 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝜃 = 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 n2=sinθ1/ sinθ2 Index of refraction for the glass n2 Position 1: sin29/sin48=0.652 Position 2: sin29/sin48=0.647 Position 3: sin29/sin48=0.652 Average of n2: (0.652+0.647+0.652)/3=0.6503

Analysis In the first part of the experiment for the reflection, we were able to determine that the incident angle of light to the surface of the mirror from the normal line is equal to the reflection angle from the normal line. This is called law of reflection. We were also be able to see that the object distance is equal to image distance in a plane mirror. The second part of the reflection experiment verified the reflection law again, in addition it has also verified that the image size is equal to the object size in a plane mirror. Then we determined the number of images of an object for the situation which there are two plane mirrors are placed with an angle to each other. We determined the number of images when the mirrors were at 60o, 90o,120o. At the condition where the mirrors are perpendicular to each other,

we were able to so 3 images. As we decreased the angle from 90o to 60o, we have observed 5 images. As the angle between the mirrors become smaller than 90 o, there is an increase in the number of images. As we reach 0o and two mirrors are parallel to each other, there will be infinite number of images in the mirrors. On the other hand, if the angle between mirrors become larger than 90o, there will be a decrease in the number of images, and in our case form the angle of 120 o, there were only 2 images in the mirrors. As we reach 180 o and two mirrors are along each other, there will be 0 image in the mirrors. On the second part of this experiment, we were able to determine another property of the light which was refraction. As light travels through different medium, there will be reflection of the light. In the case of our experiment, the light traveled form a lower density medium, which was air, to a higher density medium, which was a thick glass. We have observed that under this condition the angle of refraction is larger than angle of incident. CONCLUSION/QUESTIONS a. What are the possible sources of error in the experiment? What effect does the thickness of the mirror have on the experiment. Possible errors can be:  The thickness of the mirror  Not drawing the exact correct sight line.  Measurement errors for the angles and object size (may measure by couple of mms or 0.1degrees off because of reading error.  Collected data might have gotten bigger/smaller scale due to copying the original data There were also minor errors in the case of incident and reflection angle. The e(%) is calculated in the calculation part. Because the e(%) was fairly a small number, the collected data is reliable. These minor difference for the image size or image distance has happened to errors that is discussed above. In the case of thin glass, the image cannot be observed in the surface of the mirror as perfect as the image in a thick glass. A mirror is made by silvering or spraying a layer of silver or aluminum onto the back of a sheet of glass. We will be able to observe better and sharper image in the case of thick glass. b. What is meant by saying that the image is "behind the mirror"? This means that the image is virtual. The image formed by a plane mirror is always virtual. It means that the light rays do not actually come from the image.

c.

To take a clear picture of an image in a plane mirror, should the camera be focused on the image or on the surface of the mirror? Explain. The camera should be focused on the image. If it is focused on the surface of the mirror, the image will be blurry. Even though that there is no real image in plane mirrors, the virtual image is at some distance from the surface of the mirror. We are interested in the light rays, which go from object through reflection to the camera. That is the reason that the camera should be focused on the image, not the surface of the mirror.

d. Comment on the number of images observed versus the angle between the two mirrors in Reflection steps 3 & 4. As the angle between the mirrors become smaller than 90o, there is an increase in the number of images. If the angle between mirrors become larger than 90o, there will be a decrease in the number of images. In the case of 0o there are infinite images, and in the case of 180o there is no image. e.

Under what conditions is the angle of incidence smaller than the angle of refraction? Consider what happens in these conditions as the incident angle is increased from 0 towards 90o. According to the Snell’s Law of Refraction, 𝑛 𝑠𝑖𝑛𝜃 = 𝑛 𝑠𝑖𝑛𝜃 . When the angle of incident is smaller than the angle of refraction (𝜃 > 𝜃 ), then the 𝑠𝑖𝑛𝜃 > 𝑠𝑖𝑛𝜃 . This means that n1>n2. In this case, light moves from an optically denser medium to an optically rare medium. In the case where n1>n2, if the angle of incident gets larger, the refracted ray will make an angle of 90o with the surface normal. If 𝜃 is increased beyond that angle, then there is no refraction of the light going out through the medium. In this case, all the light incident on the interface is reflected back into the incident medium. The smallest angle of incidence at which total internal reflection occurs is called https://www.optics4kids.org/what-is-optics/refraction/snell-s-law,-reflection,-and-refraction the critical angle. Conclusion: By completing this experiment, we were able to verify the reflection law. We have determined that incident angle of the light to a surface is equal to the reflected angle. We have observed that in a plane mirror the image size and image distance are equal to object size and object distance. On the last part of the experiment, we have observed the refraction of the light. We were able to calculate the index number for the glass. All collected data has verified all the mathematical relationship in reflection law and Snell’s law for refraction....