1. Physics for Scientists and Engineers II, Summer Semester 2009 1 Lecture 24: July 20 th 2009 Physics for Scientists and Engineers II

2. Physics for Scientists and Engineers II, Summer Semester 2009 2 Chapter 36: Image formation by Flat Mirrors Ray tracing using the law of reflection The reflected light rays appear to come from this “image”. The image is not really there (the light rays do not really come from this point).  It is called a “virtual image”. Image distance Object distance

3. Physics for Scientists and Engineers II, Summer Semester 2009 3 Flat Mirrors: Magnification “+” sign means image is upright

4. Physics for Scientists and Engineers II, Summer Semester 2009 4 Image formation by Spherical Concave Mirrors Principal Axis Paraxial rays (small angle with principle axis) meet at one point to form a REAL image. Rays with greater angle do not meet exactly at that point (spherical aberration).

5. Physics for Scientists and Engineers II, Summer Semester 2009 5 Image formation by Spherical Concave Mirrors

6. Physics for Scientists and Engineers II, Summer Semester 2009 6 Image formation by Spherical Concave Mirrors

7. Physics for Scientists and Engineers II, Summer Semester 2009 7 Focal Point of Concave Mirror For p >> R (very far away object): Rays come in parallel and meet at F (focal point).

8. Physics for Scientists and Engineers II, Summer Semester 2009 8 Image formation by Spherical Convex Mirrors

9. Physics for Scientists and Engineers II, Summer Semester 2009 9 Sign Conventions for Mirror Equation PositiveNegative Object Location (p)Real Object (in front of mirror) Virtual Object (behind the mirror) Image Location (p)Real Image (in front of mirror) Virtual Image (behind the mirror) Image height (h’)Image is UprightImage is Inverted Focal Length (f) and Radius (R) Mirror is ConcaveMirror is Convex Magnification (M)Image is UprightImage is Inverted

10. Physics for Scientists and Engineers II, Summer Semester 2009 10 Real or Virtual Images ? Generally, objects are real (but there are exceptions to that)  Let’s assume p > 0 Concave mirror: f > 0Convex mirror: f < 0

11. Physics for Scientists and Engineers II, Summer Semester 2009 11 Example – Spherical Mirror A: A concave mirror has a radius of curvature of 100cm. A person stands in front of the mirror at a distance of 140cm. Where is the mirror image of the person? Is the mirror image upside down or upright? Is it real or virtual ? The person is wearing a t-shirt with“U of Utah” written on it in 5.0cm tall letters, how large will the letters appear in the image? Answer: Given are p = + 140 cm ; f = + R / 2 = + 50 cm ; h = + 5.0cm

12. Physics for Scientists and Engineers II, Summer Semester 2009 12 Example – Spherical Mirror B: The person stretches out her arm towards the mirror. The mirror image is then stretching out it’s arm towards the person. Is it possible for the person to “touch” with the tip of her index finger the tip of the index finger of her image? If so, where exactly will the tip of her index finger be? Answer: Given are f = R / 2 = 50 cm. For the condition described to be possible, Both the index finger and it’s image must be at the same location:  q=p

13. Physics for Scientists and Engineers II, Summer Semester 2009 13 Example – Spherical Mirror C: Now, the mirror is replaced with a convex mirror of the same radius. Answer the questions from part A again. Answer: Given are p = + 140 cm ; f = - R / 2 = - 50 cm ; h = + 5.0cm

14. Physics for Scientists and Engineers II, Summer Semester 2009 14 Review Problem1 Compare the intensity of these two light sources: 1)An ordinary 100W light bulb that converts 80% of the power into heat and 20% into light, which radiates in all directions equally. 2)A laser beam from a laser with 10.0mW light output with a 2.00mm beam diameter. Assume the laser has no beam divergence (radius of the beam is constant). a)5.00cm away from the light source. b)10.0m away from the light source. a) Answer:

15. Physics for Scientists and Engineers II, Summer Semester 2009 15 Review Problem1 b) Answer:

16. Physics for Scientists and Engineers II, Summer Semester 2009 16 Review Problem2 R1 Pure L (no resistance) SW x R2 1)Describe what happens to the currents when the metal bar is pulled across the tracks. 2)Describe what happens to the current when suddenly the switch is opened. (Neglect the inductance effects of the big loop (metal track+ bar)

17. Physics for Scientists and Engineers II, Summer Semester 2009 17 Review Problem2 R1 Pure L (no resistance) SW x R2