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(8%) Problem 5: When a h = 8.5 cm long pencil is arranged perpendicular to a con

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Question

(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