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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. We need two equations Mirror equation F = focal length of the mirror Do = distance to object Di = distance to the image We are using reciprocals here! 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 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 Lets do it 1/f = 1/do + 1/di So we have : 1/(15.2 cm) = 1/(45.7 cm) + 1/di Use the equation : Using the inverse key on our calculator gives you : 0.0658 = 0.0219 + 1/di 0.0439 = 1/di, Then Di = ? di = 22.8 cm Let’s continue What do we know F = 15.2 cm Do = 45.7 cm Di = 22.8 M=? Ho = 4cm Hi = ? Step 2 Solve for magnification M = hi/ho OR - di/do So, M =hi /(4.0 cm) OR -Di/Do = - (22.8 cm)/(45.7 cm) This gives us M = -.498 Remember h0= (4.0 cm) Let’s try one What do we know F = 15.2 cm Do = 45.7 cm Di = 22.8 M = -.498 Ho = 4cm Hi = 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 Remember: What do we know F = 15.2 cm Do = 45.7 cm Di = 22.8 M = -.498 Ho = 4cm Hi = -1.99 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 f is + if the mirror is a concave mirror f is - if the mirror is a convex mirror di is + if the image is a real image and located on the object's side of the mirror. di is - if the image is a virtual image and located behind the mirror. hi is + if the image is an upright image (and therefore, also virtual) hi is - if the image an inverted image (and therefore, also real) 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 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