(8%) Problem 5: When a h = 8.5 cm long pencil is arranged perpendicular to a con
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(8%) Problem 5: When a h = 8.5 cm long pencil is arranged perpendicular to a convex mirror's optical axis at a distance of 29 cm from the mirror, its image is 0.75h cm tall * 50% Part (a) What is the mirror's focal length (include sign if negative), in centimeters? Grade Summary Deductions Potential f-11.33 20% 80% cosO cotan0asin0 tan() | | ( acos0 sinhO Submissions Attempts remaining: 3 (10% per attempt) detailed view sin 78 9HOME atanOacotan) si cosh0tanhO 10% 10% coho 0 END Degrees Radians O BACKSPACE DEL CLEAR Submit e up Hits: 0 for a 0% deduction . Hints remaining Feedback: 5% deduction per feedback 50% Part (b) How tall is the pencil's image if the pencil is moved to a distance of 59 cm from the mirror (include sign if negative)?Explanation / Answer
use from the formula of magnification
m = h'/h = v/u
height of the image h' 0.75 * 8.5 = 6.375 cm
h/h = m = v/u = 6.375/8.5 = 0.75
here object distance u = 29 cm
image distance v = um = 29* 0.75 = 21.75 cm
focal length -1/f = -1/u - 1/v
1/f = -1/29 - 1/21.75
f = -12.42 cm
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part B:
for u = 59 cm
f = -12.42 cm
v = ?
-1/12.42 = -1/59 -1/v
v = 15.75 cm
then
maginification m = -v/u = h'/h = 15.75/59
m = h'/h = 0.266
h' = height of the image = 0.266* 8.5
h' = 2.26 cm
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