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Experiment 2 Mirrors

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AnalysisThe experiment encompasses topics on optics particularly on plane and spherical mirror. Generally, a light, like sound, behaves like a wave. Thus, it also has properties like reflection, refraction, interference, and diffraction. In this particular experiment, light is studied and treated like wave with the use of a plane and spherical mirror.Mirrors are used widely in optical instruments for gathering light and forming images since they work over a wider wavelength range and do not have the problems of dispersion which are associated with lenses and other refracting elements.For this experiment, materials that are necessary are plane mirrors, a pin, concave mirrors, candle, ray table, three-surfaced mirror, meter stick and optics table with light source. A labeled presentation of the experimental materials is shown to the left (Fig. 2-1).Figure 2-1. Experimental Materials

In the first part of the experiment, law of reflection is being proven. This law states that the reflected ray lies in the plane defined by the incident ray and the surface normal, and that in the plane the anglethe reflected ray makes with the normal is equal to thatmade by the incident ray (See Figure 2-2 below). A beam of light is allowed to pass through a plane mirror. As what is seen, the light reflects back at the same angle from where the light strikes the mirror. Difficulty on arranging the plane mirror is observed to have a perfect equal angle. The angle from where the light strikes is called the angle of incidence while the angle from where the light reflects back is called the angle of reflection. If wrong set-up is made, it is noticed that the difference between the angle of reflection and the angle of incidence increases as the angle is increased upon rotating the mirror. The data below (See Table 2-1) shows the resulting angle of incidence and its corresponding angle of reflection. As seen, the angles are exactly equal, thus, the law of reflection is completely proven.Figure 2-2. Experimental Materials

Table 2-1. Laws of Reflection

TrialAngle of IncidenceAngle of Reflection

11010

23030

35050

47070

The image to the left (See Fig. 2-3) shows the actual reflection of the light in the experiment. As seen, the angle of incidence and the angle of reflection form are tantamount to each other which is at 70o measured from the normal line to the plane mirror.Figure 2-3. Reflection of angle beam at 70o

For the next part, the number of images formed when two plane mirrors are arranged in such a way that they are facing each other, having a common edge and also a common angle between them are determined. The set-up of this part is well presented below.Mirror 1Mirror 2Angle between them

When two plane mirrors face each other, various reflections of images are being seen on both sides of the mirror and is given by the equation

where I is the number of reflected images and is the angle between two plane mirrors. With respect to our data, our result is somehow different from what is theoretically observed. In the data below (See Table 2 also associated with a graph), it is seen that when the angle is still big, the number of reflected images can still be counted accurately but as the angle is decreased, the possibility of miscounting also increase. It is due there is maximum figures in the mirror which a human eye can see is already attained.Table 2-2. Number of Images

TrialsAngle between plane mirrorsNumber of Images Formed

ObservedCalculated

1102435

2151623

3301011

44587

56065

67544

79023

812022

The angle determines the number of image that can form on the two plane mirrors. The image below (Figure 2-4) shows that a degree of 60oC angle between two mirrors would make 5 images which follow the equation 1. In the figure above shows the experimental and theoretical image of the number of figure can be seen for a 60o between two mirrors. As seen, the image is reflected as many as it can be depending on the angle between the facing mirrors. It is observed that it is multiplied according to a complete rotation of 360o, with respect to the angle between the mirrors. However, the number should be decreased by one because that one represents the real object.Figure 2-4. Experiment Part 2, Diagram on left side and actual experimentation on right side.

In the graph, the violet curve line shows the theoretical number of images formed while for the observed, it is presented by a blue line. As seen, greater miscounting increase as the angle is decreased. It is observed that the images formed are getting smaller and smaller that comes a point that the image formed is cannot be seen by naked eye. Also, the brightness of the image affects the number of images that can be seen by naked eye. Since the experiment has dark surroundings, then it is possible to get a far result than what is expected.

Graph 2-1. Number of images formed vs. Angle obtained by calculations and experimentally.

On the third part of the experiment, the focal length of both concave and convex mirror is obtained based on the reflected light observed on it. These are done through mirror ray tracing. By this method, an imaginary line which is the optic axis is drawn at the center of the mirror perpendicular to its axis. When beam of lights are reflected by the mirror, it all intersects at a common point (only when extended for convex mirror). This point to the surface of the mirror through the optic axis is the focal length of the mirror. By convention, for convex mirror the said intersection point is located behind the surface of the mirror while for the concave mirror it is located at front.For convex mirror, a ray parallel to the optic axis and one incident ray passing through and reflected back from the center of the mirror are extended. The resulting light rays are back-drawn by projecting it from the rays. The distance from the common point behind the surface of the mirror located at the principal axis to the mirror itself is the actual measure of the focal length. So as with for the concave mirror, the distance between the common point formed at the front of the mirror at the principal or optical axis determines the focal length of the mirror.Figure 2-6. Concave mirror focal length determinationFigure 2-5. Convex mirror focal length determination

The focal length of curved mirrors are said to be twice the radius of the circle fitted to the surface of the mirror. It is given by the equation below. The image is also presented to allow us to have a better understanding of this theorem.

R

Figure 2-6. The focal length based on the circle from where the arc of is segmented

Based on the image above, it can be said that the surface of a mirror can be described as an arc segmented from a circle having a radius R.Based on the focal length obtained from the actual and experimentally, the values are very consistent with each other. It means that experimentation is done correctly. Table 3. Determination of Focal Length and Radius

Types of MirrorConvexConcave

Focal Length, f67

Experimental radius of curvature, R expt1214

Actual radius of curvature, R act1213.5

Percentage Error0.0%3.64%

As additional information, for concave mirrors, when the object is within the range of the focal length, the formed image is enlarged, erected as is, and formed behind the mirror as virtual image. While on the other hand, when the object is outside the focal range, it is formed as a real image, in front of the mirror, minimized and inverted. This scenario occurs in the next part of the experiment.Figure 2-7. Part 3. Focal length determination for spherical mirrors (concave on left and convex on right)

The image above shows the actual experimentation in determining the focal length of the spherical mirror. The convex mirror is presented to left while the concave mirror is at the right.In the fourth and last part of this experiment, a spherical mirror is used to reflect back an objects image through a detector which is a plane white surface board.As we all know, lights allows us to see object. When the light strikes the object, its color, shape and depth can be seen. When a spherical mirror is brought in front of the object, the light travels from the object to the mirror, and is then reflected. If a detector is present, the reflected image is seen at a certain degree of clarity and size. The image is also seen to be inverted.

Figure 2-8. Theoretical observation on reflection image of an object (Part 4)The clarity of the image and its size is related to the focal length of the spherical mirror. The image would only be clear until when the distance required between the mirror and the detector (the reflected image) is attained at a known and distinct measure of distance between the object itself and the mirror. It is given that the sum of the reciprocal of the object distance and the image distance to the mirror is equal to the reciprocal of mirrors focal length. It is described by the equation below.

It is also given that when the sign of q is negative, virtual image is seen which means that the reflected image is behind the spherical mirror. On the other hand, when it is positive, the image is called a real image and is located at front of the mirror. Also, the f and R are positive when the spherical mirror is concave and will be negative if the mirror is convex. In the experiment, we are dealing with real images and concave mirror.This part is divided into four parts, namely the (a) object distance is greater than the image distance, (b) image distance is greater than the object distance, (c) object distance is equal to image distance, and (d) object distance is very far that it is assumed to approach infin

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