Optical Instruments — Question 1

Question 1

Close camera focus requires extension beyond the infinity setting

A camera is modeled by a thin lens of focal length 50 mm and a movable sensor. An object plane is 2000 mm in front of the lens. The sensor width is 36 mm; ignore distortion and vignetting.

1. Find the required image distance and extension from infinity focus.

2. Find the transverse magnification and width of object space recorded across the sensor.

Question 1 - Solution

Close camera focus requires extension beyond the infinity setting

(a) Method and calculation

$$q=\frac{fp}{p-f}=\frac{50(2000)}{1950}=\boxed{51.2821\,\mathrm{mm}}.$$$$\boxed{\Delta q=q-f=1.28205\,\mathrm{mm}}.$$

(b) Interpretation and further calculation

$$\boxed{m=-q/p=-1/39}.$$$$\boxed{W_O=W_{\mathrm{sensor}}/|m|=36(39)=1404\,\mathrm{mm}}.$$

Physical check

The sensor lies slightly farther from the lens for a finite-distance object than for a distant scene.