The rear window of a car has a size of 120 , | vedclass

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Question

(D) Let the width of the rear window be $W = 120 \, cm$ and the height be $H = 45 \, cm$. The distance from the driver to the rear window is $d_1 = 2

Vedclass · Accepted Answer

$(20 \, cm 	imes 7.5 \, cm)$

Vedclass · Answer

(D) Let the width of the rear window be $W = 120 \, cm$ and the height be $H = 45 \, cm$. The distance from the driver to the rear window is $d_1 = 2 \, m$. The mirror is placed at a distance $d_2 = 0.5 \, m$ in front of the driver. The image of the rear window is formed at a distance $d_2 = 0.5 \, m$ behind the mirror. Thus,the total distance from the driver to the image of the rear window is $D = d_1 + d_2 + d_2 = 2 + 0.5 + 0.5 = 3 \, m$.Using similar triangles,the ratio of the mirror size $(w, h)$ to the window size $(W, H)$ is equal to the ratio of the distance of the mirror from the driver to the total distance of the image from the driver:$\frac{w}{W} = \frac{d_2}{D} \Rightarrow w = W 	imes \frac{0.5}{3} = 120 	imes \frac{1}{6} = 20 \, cm$$\frac{h}{H} = \frac{d_2}{D} \Rightarrow h = H 	imes \frac{0.5}{3} = 45 	imes \frac{1}{6} = 7.5 \, cm$Therefore,the minimum size of the mirror is $(20 \, cm 	imes 7.5 \, cm)$.

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