Physics Refraction Lab

Part A: Refer to the Protocol / Instructions of Refraction lab including Formulas + Theory

Table 1* Results of 6 Trials of light rays shining through the rectangular slab Trial Incident Distance between Measured Calculated sin 0 sin@2 angle 01 reflected rays d, refracted refracted for measured cm angle 02m, angle 02, 1 10 0.7cm 6.50 0 6.47 0 0.1730 0.113 0 2 20 1.1 cm 13.00 o 12.830 0.3420 0.224 3 30 1.7 cm 19.00 18.94 0.50 0.3260 4 40 2.5 cm 24.50 24.670 0.6430 0.4140 5 50 2.9 cm 30.00 29.830 0.7660 0.50 6 60 3.6 cm 34.50 34.210 0.8660 0.566Insert the photo of the laser beam passing through the rectangular slab you took for the first incident angle. Incident rays, refracted rays and emergent rays should be clearly visible. . Use a ruler and a protractor to draw a scaled diagram showing the light path through the rectangular slab for the first angle of incidence you used; all angles should have the values you measured. Label them. . Are calculated values for 62 the same as the measured values? Which ones do you consider as more accurate? . Use Excel to sketch the graph sin 62 [on the vertical axis] versus sin 91 [on the horizontal axis] and to draw a line passing through [or closest by] all points. Include the graph below. Label and appropriately scale the axes, title the graph and include the equation of the trendline. Identify the slope of the line, then calculate the index of refraction n ofthe prism. . Compare your calculated index of refraction with a typical value for the index of refraction for acrylic. Discuss possible sources or errors. Purpose Investigate the behaviour of light rays as they pass through rectangular and equilateral prisms. Determine the index of refraction for the material the prisms are made of. Observe total internal reflection. Equipment Geometric optic kit, protractor, pins, Vernier caliper, ruler, white screen Background Theory According to the ray model of light, light travels through a vacuum or a transparent material in straight lines called light rays. The speed of light in a material is v. The index of refraction of the material is n, n= When light crosses the boundary between two different transparent materials, with indices of refraction m and n2: part of the light reflects from the boundary, obeying the law of reflection. This is how you see the reflections from pools of water or storefront windows, even though water and glass are transparent. part of the light enters the second medium. The transmitted ray changes direction as it crosses the boundary. The transmission of light from one medium to another, but with a change in direction, is called refraction. Figure bellow (from the textbook) shows an example of refraction. The incident ray makes an angle 01, called the angle of incidence, with the normal to the refracting surface. The refracted ray makes an angle 0, with the normal to the refracting surface called the angle of refraction. (c) Refraction from higher-index medium to (b) Refraction from lower-index medium to lower-index medium higher-index medium Angle of Angle of Normal refraction incidence Weak reflected ray Refracted n n ray boundary. Refracted Weak reflected ray ray Angle of Angle of incidence refraction n, sin 0, =n, sin 0, Reflection and refraction through a rectangular plateWhen light enters a rectangular prism made of a transparent material, some of the light is reflected on the first surface of the plate, while the rest gets refracted into the prism. Part of the refracted ray is reflected off the back surfaces of the prism, so two reflected rays separated by the distance d are observed. This separation d depends on the thickness of the prism t and the angle of incidence. Fig. 1 Geometry of the setup for TIR from Physics Labs for Scientists and Engineers North Carolina State University. https://www.webassign.net/labsgraceperiodcsuplseem2/lab_10/manual.html. Consider m = 1.00 the index of refraction for air and n for the plastic plate: sind =nsind, i sin 0,= sin d n From geometrical consideration: in AAEC, d = EC =ACsin( er. For example, when a horizontal ray hits a right triangular acrylic prism perpendicular on one of its legs, it passes straight through, undeviated. Inside the prism, it hits the hypothenuse side of the prism at an angle of incidence of 45". This angle is greater than the critical angle for the acrylic-air surface, so the light is totally internally reflected. Since the angle of reflection is the same as the angle of incidence, the reflected ray on the hypothenuse moves off at 45" from normal on the hypothenuse side, so the total deviation of the beam of light is 90". 90" Deviation of a beam of light Fig. 2 Diagram for TIR inside a right isosceles acrylic prism from Saint Mary's Halifax University, Physics Demos https://demos.smu.ca/demos/optics/71-internal-reflection n sin 8,=1 Pre-lab question 1: Calculate the critical angle for an acrylic-air surface when the index of refraction for acrylic is 1.54 SAFETY Lasers can cause eye damage. Avoid exposure never mount the laser at eye-level or never point it toward someone else or reflective surfaces no matter how careful you are. Turn off the laser when not in useEXPERIMENT You will use an acrylic slab (rectangular prism) and a right isosceles triangular prism to study the refraction of light from their surfaces. You measure the angles of incidence, calculate angle of refraction in order to determine the index of refraction of the materials the slab and prism are made of. Then, you investigate the conditions to obtain total internal reflection inside the prism. PROCEDURE A: Reflection and refraction through a rectangular acrylic prism The angle of refraction is examined experimentally by measuring the separation between the two reflected rays through the prism as shown below. Fig. 3 TIR at glass-air surface from Physics Labs for Scientists and Engineers. North Carolina State University. https://www.webassign.net/labsgraceperiodcsuplseem2/lab_10/manual.html. 1. Measure the thickness t of the rectangular acrylic block with the Vernier caliper, then place onto the middle of the protractor sheet. 2. Place the white screen on the same side of the prism as the laser source, so that you can capture the reflected rays; once you find a proper position, do not move it. 3. Shine the laser beam on the front surface of the plate at an angle of incidence 0 of 10. Notice two red spots produced by the reflected ray on a screen and measure the distance d between them. 4. With the protractor, measure the angles 01, 0. 5. Take a screenshot of your setting that captures the incident, refracted and reflected rays to include it in your report. 6. Draw the diagram on your lab report showing the light path for this angle of incidence; label all angles of interest. 7. Repeat steps 3and 4 five more times by changing O in increments of 10" and record the data in your Table 1. 8. For each incident angle, calculate reflected angle 6, by using d tan d = tan 2t cos 0 9. Determine sin 0 for each calculated value Or10. Sketch the graph sin , (on the vertical axis) versus sin O (on the horizontal axis). Use Excel to draw a line passing through (or closest by) all points and include the equation of this trendline. The index of refraction n of the plate is the reciprocal of the slope of the line. sin 0,= - sin #, n 11. Compare the calculated index of refraction with typical values for the index of refraction of optical materials (from your research). Discuss possible sources of error. Pre-lab question 2: What measurements do you take when working with the rectangular acrylic plate? PROCEDURE B: Total internal reflection by a triangular prism 12. Place the right isosceles triangular acrylic prism with one short side parallel to the base of the protractor sheet so that the laser beam is perpendicular to it and TIR occurs on the long side inside the acrylic prism. Fig. 4 TIR from Saint Mary's Halifax University, Physics Demos https://demos.smu.ca/demos/optics/71-internal-reflection 13. Rotate the source of laser light about the prism to increase the incident angle of the laser beam hitting long side until you obtain an angle of refraction of 90" and the refracted beam is transmitted along the long side of the prism; further increasing the angle of incidence will turn the beam totally inside the prism - this is total internal reflection. Increasing 01 further leads to internal reflection of the beamd Setting for critical angle with beam of light still emerging from the prism 14. Take a photo of your settings, showing the emergent ray parallel to the long face of the prism. 15. With the protractor, measure the incident angle 0 on the front face of the prism and the incident angle O on the long side of the prism; this is the critical angle; record the data in your report. 16. Calculate the refractive index n by using sin 17. Compare your result with the value for n you obtained for step 10. 18. Calculate the angle of refraction on the front side from the geometry of the prism 0,=0.-45 then use calculated n to find the angle of incidence Of from Snell's law sind =nsind, Compare it with the one you measured