TI-Nspire™ Activities: Physics
May 6, 2008 through May 13, 2008
Focusing on Light
| Problem 1 – Reflection from a parabolic mirror |
|
| Step 1: Students should open the file PhysWeek15_focusing_light.tns and read the first two pages. Page 1.3 shows a group of five plane mirrors reflecting a series of light rays. The dotted lines in the image are incident light rays; they cannot be adjusted. Students should adjust these mirrors so that the reflected light passes through the single point marked A. It may take students several tries to align the rays correctly. They should then answer question 1 on page 1.4. Q1. Describe the general shape formed by the plane mirrors when the reflected light passes through point A. A. The mirrors form a parabola with a gentle curvature, as shown on the right. “Curved” or “concave” are also acceptable answers. Encourage students to examine the way the light rays reflect off of each individual mirror. They should notice that the reflections off of each plane mirror follow the same rules of reflection they are familiar with. |
|
| Step 2: Page 1.5 shows a flexible parabolic mirror. The mirror will retain its parabolic shape even if students make it wider or narrower. The incident light ray is shown as a dotted line. The reflected ray is a thin solid line. A tangent to the parabolic mirror has been drawn in and is representative of a flat mirror at point P on the curve. Students should drag point P around the mirror and observe how the reflected light ray changes. They should then answer question 2 on page 1.6. Q2. Describe what happens to the reflected ray as you move point P along the parabolic mirror. A. The reflected ray seems to rotate around a single point. |
|
| Step 3: Page 1.7 contains an image of a second parabolic mirror with a number of parallel incident light rays striking the mirror in different locations. The multiple incident rays help identify important characteristics associated with reflected rays. Have students drag points P, Q, and R along the mirror and observe how the reflected rays move. Students should then answer questions 3–5 on pages 1.8 and 1.9. Q3. Describe what happens to the reflected rays as you move points P, Q, and R along the parabolic mirror. A. The reflected rays rotate around a single point, which is the point at which all three rays intersect. Q4. Adjust the width of the parabola. How does this affect the reflected rays as you move the three points? A. Regardless of the width of the parabola, the reflected rays always converge on a single point. This point moves further away from the bottom of the parabola as the parabola gets wider. Q5. Based on your observations, make a general statement about how parabolic mirrors reflect incident light rays that are parallel to the parabola's line of symmetry. A. A parabolic mirror reflects incident light rays to a single point. Explain to students that this point is called the “focal point” of the mirror. Encourage students to manipulate the simulation to explore the relationship between the curvature or width of the mirror and the location of the focal point. |
|
| Problem 2 – Reflection from a semicircular mirror | |
| Step 1: Page 2.1 shows a semicircular mirror. The incident light ray appears dotted. The reflected ray is a thin solid line. A tangent to the parabolic mirror has been drawn in and is representative of a flat mirror at point P on the curve. Have students drag point P around the mirror and watch how the reflected light ray changes. |
|
| Step 2: Page 2.2 contains an image of a second semicircular mirror with three incident light rays and the corresponding reflected rays. Have students drag points P, Q, and R along the mirror and observe the results. Students should then answer questions 6 and 7 on pages 2.3 and 2.4. Q6. Based on your observations, make a general statement about how semicircular mirrors reflect incident light rays that are parallel to the mirror's line of symmetry. A. The reflected rays do not intersect at a single point. Q7. In a reflecting telescope, a curved mirror reflects incident light rays toward a single point in the eyepiece. Are these mirrors most likely parabolic mirrors or semicircular mirrors? Explain your answer. A. They are most likely parabolic mirrors. Semicircular mirrors do not reflect light toward a single point, but parabolic mirrors do. |
|
| Problem 3 – Reflection of non-parallel incident rays | |
| Step 1: Page 3.1 shows a parabolic mirror reflecting incident light
rays originating from a single object. The incident rays are not
parallel to one another. Have students drag points P, Q, and R around
the parabolic mirror and observe the results. |
|
| Step 2: Next, have students move the object around the screen and observe the results. Then, have students answer question 8 on page 3.2. Q8. Describe how the parabolic mirror reflects light coming from a single object that produces incident rays that are not parallel. A. The reflected rays do not converge on a central point. Encourage students to discuss the significance of this. They should realize that it is impossible to use a parabolic mirror to produce a real image of an object placed within or close to the curvature of the mirror. As an extension activity, you can challenge students to move points P, Q, and R so that the three reflected rays meet at a single point. You can also ask students to see if they can place the object in a position so that all the reflected rays emerge parallel. |
|