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Chapter 31: Problem 27

A magnifying glass enlarges print by \(50 \%\) when it's \(9.0 \mathrm{cm}\) from a page. What's its focal length?

Short Answer

Expert verified
The focal length of the magnifying glass is 37.5 cm.

Step by step solution

01

Convert Magnification Percentage to Whole Number

The magnification, denoted by m, is the degree to which the size of an object is increased. In this case, the magnification is \(50\% \) or 0.50, which is equal to a magnification of 1.5 times.
02

Calculate Image Distance

According to magnification formula, m = -d_i / d_o, where d_o is object distance and d_i is image distance. The magnifier is constructed in such a way that it forms an image at the distance of distinct vision, which is approximately 25 cm. For a relaxed eye, the image is formed at infinity. Hence, for maximum magnification we consider image distance, d_i as \(-\infty\). Therefore, taking the absolute value of both sides, you get m = d_o / |d_i|, substituting the value of m and |d_i|, we get d_o = m * |d_i| = 1.5 * 25 cm = 37.5 cm.
03

Compute Focal Length

Using the lens formula, 1/f = 1/d_o - 1/d_i, where f is focal length, d_o is object distance and d_i is image distance. We replace d_i with \(-\infty\), which simplifies to 1/f = 1/d_o. Therefore, the focal length f = d_o = 37.5 cm. Note that the focal length of a magnifying glass is usually given in centimeters.

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