This seems pretty straightforward, but I was hoping to get a second opinion. Tha

Question

This seems pretty straightforward, but I was hoping to get a second opinion. Thanks

Two new pencils are carefully balanced on a table top. One is shorter than the other. The shorter pencil is exactly half the length of the longer pencil. An observer looks at them from along the line joining the bases of the pencils, as indicated in the figure below. The distance x = 15cm. If the observer's eye is at d = 15cm, which image shown above corresponds most closely to what would be seen? A B C D If the observer's eye is at d = 30cm, which image shown above corresponds most closely to what would be seen? A B C D F If the observer's eye is at d = 200cm, which image shown above corresponds most closely to what would be seen? A B C D E

Explanation / Answer

tan A = L/(x+d) = (L/2) / d

=> 2d = x+dÂÂ

=> x = d

 tanA1 = L/x+d

tanA2 = L/d+d

for x = d , A1 = A2 so both pencil's tips seen hence both equal.

for d<x  , A1<A2 => only smaller pencil seenÂÂ

for d>x , A1>A2 => larger pencil also seen and smaller seen small in size

a) for d = 15 (x = d)

E

b)d = 30 (d>x)

D

c) d = 200

C

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