REFRACTION, Slides of Law

Download REFRACTION and more Slides Law in PDF only on Docsity! Brooklyn College 1 REFRACTION Purpose a. To study the refraction of light from plane surfaces. b. To determine the index of refraction for Acrylic and Water. Theory When a ray of light passes from one medium into another one of different optical density, it undergoes a change of velocity and a consequent change in direction. Figure 1 is an example of refraction. The incident ray makes an angle with the normal to the refracting surface called the angle of incidence, i. The refracted ray makes an angle with the normal to the refracting surface called the angle of refraction, r. In Figure 1, if the incident medium is vacuum or free space, the speed of light is c. (The speed of light in air is very nearly equal to that in vacuum.) If the speed of light in the refracting medium v is less than the speed of light in the incident medium, the refracted ray bends towards the normal so that angle r is less than angle i. (If the speed of light v in the incident medium is less than that of the speed of light in the refracting medium, the refracted ray would bend away from the normal. This can be seen in Figure 1 if the light path is reversed. The refracted ray now becomes the incident ray, and the incident ray is now the refracted ray, bending away from the normal.) Snell’s Law: If the incident medium is a vacuum (or air, approximately), the basic law of refraction is Snell’s Law according to which v c rSin iSin  (1) The ratio c/v is called the index of refraction, n, of the refracting medium: vcn / (2) Thus, Snell’s Law may be written as n rSin iSin  (3) Incident medium = VACUUM Speed of light = c Refracting medium = ACRYLIC Speed of light = v v < c Fig. 1. The refraction of light as it passes from vacuum into Acrylic. r Brooklyn College 2 It is therefore possible to characterize a medium via its index of refraction by measuring the angles of incidence i and the angle of refraction r. Finally, when light passes from one medium to the next, its frequency f does not change. The electrons in the refracting medium absorb energy from the light and undergo a vibrational motion with the same frequency. The motion of the electrons then causes reradiation of the energy with the same frequency. In any medium v = λ f. Since the speed of light in the refracting medium v is less than the speed of light c in vacuum, and its frequency f is unchanged, its wavelength λ is correspondingly reduced. Hence, the wavelength λ of light in a material is less than the wavelength λ0 of the same light in vacuum by a factor of n: . n o  (4) Experiment: There are three parts to the experiment to study the refraction of light and determination of the index of refraction. In Part I we will use an acrylic slab, part II a prism, and part III a jar of water. You are provided with the following apparatus. Apparatus Rectangular Acrylic plate, Acrylic prism, protractor, ruler, Cork board, white paper, Red Laser. Description of Apparatus You will use an acrylic slab (Fig. 2a) and prism (Fig. 2b) to study the refraction of light from their surfaces to determine the index of refraction of the materials used to make the slab and prism by measuring the angles of incidence and refraction. The beam of a laser (Fig. 2c) is used to trace the direction of light. You will also use a water jar to determine the index of refraction of water using an apparatus shown in Fig. 2d. Fig. 2: Apparatus for the experiments in this lab a. Acrylic slab a. Prism d. Water tank with sliding plates c. Red laser Brooklyn College 5 Remove the prism, and with the protractor, draw the normal at points E and F. With the ruler, draw the incident, refracted and emergent rays. Extend the incident ray JE to H. Extend the emergent beam FK backwards to L. Measure the angles i, r1, r2, e and the angle of deviation θ (angle FGH) (See Figure 4). Record the data, the value of the refractive index n, and the angle of deviation θ in Table III. (c) Repeat Part II (b) for an angle of incidence that is less than that employed in Part (a). Part III. Refraction by water In this final component of the experiment, we will determine the index of refraction of water. The apparatus used for this part of experiment is shown in Figure 5. It has a Metal Frame containing four brass sliders 1, 2, 3, 4, and a jar of water. See Figures 5 for the experimental setup. 1. Set the sliders in the slots of the frame with the arrows pointing upwards, with the corresponding numbers as shown in Figure 5. Set the jar of water on a white sheet of paper. Mount the metal frame on the jar as shown in Figure 5a. 2. Push slider 4 as far down into the water as possible. Push sliders 2 and 3 as close to the surface of the water as possible without touching the water. Finally adjust slider 1 so that the point A appears to be in line with points B and D. See Figure 5a. To confirm your sighting, shine the laser beam along the line AB. You should see the beam reflected at D. 3. Remove the frame from the water and lay it on a sheet of paper without disturbing the sliders. Mark the positions of the points A, B, C, D on the paper. You must include this work in your report after further drawing and calculation. Fig. 5a Experimental setup for refraction by water. Fig. 5b Brass sliders in frame. Brass sliders Frame Eye Water level Water Air E i n 1 2 3 4 Brooklyn College 6 Computation 1. Calculate the index of refraction of the plate from the data in Table 1 for angles of incidence, refraction, and emergence, and record in Table 1. 2. Calculate the index of refraction of the prism from the data in Table 2 for angles of incidence, refraction, and emergence, and record in Table 2. Also calculate the index of refraction from the angle of minimum deviation using Eq. 6. 3. Calculate the index of refraction of the prism from the data in Table 3 for angles of incidence, refraction, and emergent, and record in the Table 3. Determine the angle of deviation and compare this angle with the angle of minim deviation obtained in Part II (a). 4. For part III, once you have the marks of the sliders on the paper, draw the line BC (the water level). With the protractor erect a perpendicular to BC at B. Draw the lines DB and AB. Finally, measure the angles of incidence i and refraction r with the protractor. Determine the index of refraction of water via Snell’s Law. 5. Extend the line of sight AB to D' on slider 4. The apparent position of the edge of the slider 4 is at D'. Measure the apparent depth ED' and the true depth ED. Then from triangle BED' (see Figure 5a) )90(tan ' i BE ED  . (7) From triangle BED (see Figure 5a) )90(tan r BE ED  . (8) Then from Eqs. (7) and (8) we have )90(tan )90(tan' r i BE ED    . (9) Determine the ratio ED'/ED from Eq. (9) and compare with the ratio of the measured distances ED' and ED. Questions 1. In Part I, is the emergent ray parallel to the incident ray? What causes, other than experimental error, will make the emergent ray not parallel to the incident ray? 2. If you desire to shoot a fish whose image can be seen in clear water, should you aim above or below the fish? Explain by the aid of a diagram. Brooklyn College 7 Data Sheet Date experiment performed: Name of the group members: Table 1. Angles Refractive Index n Trial Incident i Refracted r1 Incident r2 Emergent e 1rSin iSin 2rSin eSin Average 1 2 3 Table 2a Vertex angle  = Angle of minimum deviation m = Angles Refractive Index n Incident i Refracted r1 Incident r2 Emergent e 1rSin iSin 2rSin eSin sin ( 𝜃𝑚 + 𝛼 2 ) sin ( 𝛼 2) Average Table 2b Angles Refractive Index, n Angle of Deviation  Incident i Refracted r1 Incident r2 Emergent e 1rSin iSin 2rSin eSin Table 3 Angles Refractive Index of water, n Incident i Refracted r1 1rSin iSin