2. Mirror equation How can we use ray diagrams to determine where to place mirrors in a telescope/ We need to know where the image will be formed, so that it can later be magnified.

3. We need two equations

4. Mirror equation F = focal length of the mirror Do = distance to object Di = distance to the image We are using reciprocals here!

5. Magnification equation M = magnification Hi = height of the image Ho = height of the object Di = distance to image Do = distance to object NOTICE it is NEGATIVE Di/Do

6. Let’s try one – from your book! A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. Determine the image distance and the image size. What do we know F = 15.2 cm Do = 45.7 cm Di = ? M = ? Hi = ? Ho = 4cm

7. Lets do it Use the equation : 1/f = 1/do + 1/d i So we have : 1/(15.2 cm) = 1/(45.7 cm) + 1/d i Using the inverse key on our calculator gives you : 0.0658 = 0.0219 + 1/d i 0.0439 = 1/d i, Then Di = ? d i = 22.8 cm

8. Let’s continue What do we know F = 15.2 cm Do = 45.7 cm Di = 22.8 M = ? Ho = 4cm Hi = ?

9. Step 2 Solve for magnification M = h i /h o OR - d i /d o So, M =h i /(4.0 cm) OR -Di/Do = - (22.8 cm)/(45.7 cm) This gives us M = -.498 Remember h 0 = (4.0 cm)

10. Let’s try one What do we know F = 15.2 cm Do = 45.7 cm Di = 22.8 M = -.498 Ho = 4cm Hi =

11. Now use the other M to find Hi M =-.498 Object height was 4 cm Final image would be 4 x -.498 = -1.99 cm

12. Remember: What do we know F = 15.2 cm Do = 45.7 cm Di = 22.8 M = -.498 Ho = 4cm Hi = -1.99

13. What do the answers tell us F+Concave mirror ALL OF OUR MIRRORS F -Convex mirror ( we don’t use convex mirrors) Di +Real image on object side Di -Virtual image behind the mirror ( we don’t use these either) Hi +Upright Hi -inverted M +larger M -smaller

14. f is + if the mirror is a concave mirror f is - if the mirror is a convex mirror d i is + if the image is a real image and located on the object's side of the mirror. d i is - if the image is a virtual image and located behind the mirror. h i is + if the image is an upright image (and therefore, also virtual) h i is - if the image an inverted image (and therefore, also real)

15. Final analysis From our answers we find: F = 15.2 cm concave mirror Do = 45.7 cm Di = 22.8 real image M = -.5 smaller Ho = 4cm Hi = -1.99 inverted

16. Note: What we have done so far applies only to mirrors When we add lenses we will use the same q equations but the LOST part will be much different