Answer
See answers.
Work Step by Step
Example 25–3 had a 12 MP sensor, 4000 by 3000 pixels.
If we assume that the sensor now has only 6 megapixels but is the same size, then the number of pixels in each direction decreases by $\sqrt{2}$. The new sensor would be 2828 pixels by 2121 pixels.
Following the work in Example 25-3, calculate the required resolution of the lens.
$$\frac{2828pixels}{32mm}=88\;pixels/mm$$
Now consider Example 25–4. As described in the example, to make an 8 by 10 inch print, the size is magnified by a factor of 8, and so the resolution decreases by a factor of 8. Find the number of pixels/mm on the print.
$$\frac{1}{8}(88\frac{pixels}{mm})=11\frac{pixels}{mm}$$
An $8\times 10$ enlargement would be on the threshold of still creating a sharp image. In Example 25-4, it is stated that making 12 by 18 inch print would be acceptable for a 12 MP sensor, which is 10.6 pixels/mm.
