Image Formation by a Convex Lens

Problema e solução em inglês, como no livro original.

A clear glass light bulb is placed 0.75 m from a convex lens with a 0.50 m focal length, as shown in Figure 16.36. Use ray tracing to get an approximate location for the image. Then, use the mirror/lens equations to calculate (a) the location of the image and (b) its magnification. Verify that ray tracing and the thin-lens and magnification equations produce consistent results.

The example is illustrated and depicts values of f = 0.50 m, do = 0.75 m, and di = 1.50 m.

Figure 16.36 A light bulb placed 0.75 m from a lens with a 0.50 m focal length produces a real image on a poster board, as discussed in the previous example. Ray tracing predicts the image location and size.

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Estratégia
Because the object is placed farther away from a converging lens than the focal length of the lens, this situation is analogous to the one illustrated in the previous figure of a series of drawings showing a woman standing to the left of a lens. Ray tracing to scale should produce similar results for d_i. Numerical solutions for d_i and m can be obtained using the thin-lens and magnification equations, noting that d_o = 0.75 m and f = 0.50 m.
Solução
The ray tracing to scale in Figure 16.36 shows two rays from a point on the bulb’s filament crossing about 1.50 m on the far side of the lens. Thus, the image distance, d_i, is about 1.50 m. Similarly, the image height based on ray tracing is greater than the object height by about a factor of two, and the image is inverted. Thus, m is about –2. The minus sign indicates the image is inverted. The lens equation can be rearranged to solve for d_i from the given information.
$d_{i} = \frac{f d_{o}}{d_{o} - f} = \frac{(0.50) (0.75)}{0.75–0.50} = 1.5 m$
16.18

Now, we use $\frac{d_{i}}{d_{o}}$ to find m.
$m = - \frac{d_{i}}{d_{o}} = - \frac{1.5}{0.75} = - 2.0$
16.19

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