Question 33.8: Camera focus. How far must a 50.0-mm-focal-length camera len......
Camera focus. How far must a 50.0-mm-focal-length camera lens be moved from its infinity setting to sharply focus an object 3.00 \mathrm{~m} away?
APPROACH For an object at infinity, the image is at the focal point, by definition. For an object distance of 3.00 \mathrm{~m}, we use the thin lens equation, Eq. 33-2, to find the image distance (distance of lens to film or sensor).
\frac{1}{d_{\mathrm{o}}}+\frac{1}{d_{\mathrm{i}}}=\frac{1}{f} (33-2)
When focused at infinity, the lens is 50.0 \mathrm{~mm} from the film. When focused at d_{\mathrm{o}}=3.00 \mathrm{~m}, the image distance is given by the lens equation,
\frac{1}{d_{\mathrm{i}}}=\frac{1}{f}-\frac{1}{d_{\mathrm{o}}}=\frac{1}{50.0 \mathrm{~mm}}-\frac{1}{3000 \mathrm{~mm}}=\frac{3000-50}{(3000)(50.0) \mathrm{mm}}=\frac{2950}{150,000 \mathrm{~mm}}
We solve for d_{\mathrm{i}} and find d_{\mathrm{i}}=50.8 \mathrm{~mm}, so the lens needs to move 0.8 \mathrm{~mm} away from the film or digital sensor.