Question

When a h = 7.5 cm long pencil is arranged perpendicular to a convex mirror's optical axis at a distance of 35 cm from the mirror, its image is 0.85h cm tall.

1.What is the mirror's focal length (include sign if negative), in centimeters?

2.How tall is the pencil's image if the pencil is moved to a distance of 44 cm from the mirror (include sign if negative)?

Answer 1

magnification,

m = 0.85 = v/u

v = 0.85u

v = 0.85* 35

v =29.75

Using mirror formula

1/f = 1/ v + 1/u

1/ f = 1/29.75 - 1/ 35

f = 198.33 cm

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b) again using mirror formula

1/198.33 = 1/ v - 1/44

v = 36.01 cm

as per magnification

m = h' /h = v/u

h' = 7.5* 36.01/ 44

h' = 6.138 cm

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