[I know I can only submit one but these are my final two questions and I\'ve bee

Question

[I know I can only submit one but these are my final two questions and I've been at it for hours, thanks.]

1) An 99.3 cm long pencil is placed along the principal axis of a convex mirror (focal length 41.3 cm), If the end of the pencil nearest to the mirror is 4.03 cm from the vertex of the mirror (within the focal point): find the length, in cm, of the image.

2) A driver looks in his side view (convex) mirror (focal length 9.27 m). If the another car is 99.2 m behind him, how far from the mirror does the image of the second car appear?

Explanation / Answer

f = -41.3 cm

for near end, p1 = 4.03 cm

1/f = 1/p + 1/q

1/-41.3 =1/4.03 + 1/q1

q1 = - 3.672 cm

far end, p2 = 4.03 + 99.3 = 103.33 cm

1/-41.3 = 1/103.33 + 1/q2

q2 = - 29.5 cm  

length = q1 - q2 = 25.8 cm ........Ans

2) f = - 9.27 cm (negative for convex mirror)

p = 99.2

1/-9.26 = 1/99.2 + 1/q

q = - 8.47 cm

Ans: 8.47 cm

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