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  4. The photograph of a house occupies an area of 1.75 cm 2 on a 35 mm slide. The slide is projected on to a screen and the area of the house on the screen is 1.55 m 2 . The linear magnification of the projector-screen arrangement, is

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Q. The photograph of a house occupies an area of $1.75\, cm ^{2}$ on a $35\, mm$ slide. The slide is projected on to a screen and the area of the house on the screen is $1.55\, m ^{2} .$ The linear magnification of the projector-screen arrangement, is

Physical World, Units and Measurements

Solution:

Area of object $=1.75\, cm ^{2}=1.75 \times 10^{-4} m ^{2}$
Area of image $=1.55\, m ^{2}$
$\therefore $ Areal magnification $=\frac{\text { Area of image }}{\text { Area of object }}$
$=\frac{1.55}{1.75 \times 10^{-4}} \approx 8857$
Linear magnification $=\sqrt{\text { Area magnification }}$
$=\sqrt{8857}=94.1$