Chapter 26, Problem 050 The owner of a van installs a rear-window lens that has

Question

Chapter 26, Problem 050 The owner of a van installs a rear-window lens that has a focal length of -0.300 m. When the owner looks out through the lens at an object located directly behind the van, the object appears to be 0.220 m from the back of the van, and appears to be 0.370 m tall. (a) How far from the van is the object actually located, and (b) how tall is the object?

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Rear-window lens Person mage of person (a) Number (b) Number Click if you would like to Show Work for this question: Units Units Open Show Work

Explanation / Answer

a) The focal length of the lense is f = -3.00 m and

image distance (v) =-0.220 m (The person and image both behind the van,so image is virtual and the image distance is negative)

To determine object distance (u) that is how far from the van the person ia actually stsnding we will employ the thin lense equation

That is

(1/u) + (1/v) =( 1/f) and

(1/u) = (1/f) -(1/v)

substitute all the values to determine the object distance u

(1/u) =(1/-0.300 m) - (1/-0.220 m)

(1/u) = 1.2121 and u =0.825 m

there the object distance is 0.825 m

b) To determine the true height of the image (ho ) we have to use the magnification equation

m =hi / ho =- v/ u

hight of the imge is given as hi =0.370 m , v=-0.220 m and u =0.825 m (from the part A)

so 0.370 m / ho = - (-0.220 m /0.825 m)

0.370 m / ho =0.26667

ho = 0.370 /0.26667 = 1.3875 m =1.39 m (approx)

therefore height of the object is 1.39 m

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