A stamp collector with a normal near point (25 cm)needs a magnifying power of 10 to examine her stamps.If one of the stamps is 2.0 cm wide,what is the angle (in degrees)subtended by the stamp when it is viewed through her magnifier?
A)23º
B)46º
C)0.80º
D)4.6º
E)1.6º

Question

Quizplus · Accepted Answer

The angle subtended by the stamp when viewed through the magnifier can be calculated using the formula for magnifying power, $M = \frac{\text{angle subtended by the image}}{\text{angle subtended by the object at the near point}}$. Given that the magnifying power is 10 and the width of the stamp is 2.0 cm, when viewed at the normal near point of 25 cm, the angle subtended by the object at the near point is $\theta = \tan^{-1}(\frac{2}{25})$. Since the magnifying power is 10, the angle subtended by the image is 10 times this angle. Calculating this directly or understanding that magnification increases the perceived size or angle by the magnification factor leads to the realization that the angle must be significantly larger than the original, making 46º the correct choice due to the magnification effect.

A Stamp Collector with a Normal near Point (25 Cm)needs