Question

Suppose that the image of a user’s face (300 mm tall) is to be relayed by a lens onto a square CMOS sensor (3.75 mm wide). The user and the sensor are separated by 500 mm.

1. To achieve the desired image size, what is the magnification of the imaging system? Be mindful of the sign convention signifying upright versus inverted images.

2. To achieve the desired image position with a single thin lens, how far from the sensor should it be placed?

3. What focal length ? should be used for this single thin lens?

4. Compute ?system = ?free space,2?lens?free space,1 for rays originating from the user and propagating through the lens to the sensor. Show your work.

5. Verify that ?system is of the correct form for an imaging system.

6. Suppose another person stands 2 m behind the primary user. Compute ? ′ system for rays originating from this new person and propagating through the lens to the sensor. Show your work.

7. Is ? ′ system of the correct form for an imaging system?

Answer 1

1. The magnification can be calculated by, (We require a real image, and a converging lens has to be used, Therefore height of image will be negative).

Therefore the required magnification is 0.0125.

2. Magnification can also be expressed in terms of distances from lens as, (just considering the magnitude)

Applying Componento-Dividendo Rule, we get,

The distance between the object and the image is the distance between the user and the sensor, substituting values we get,

Therefore the lens has to be placed at a distance of 6.173 mm from the sensor.

3. Magnification in terms of focal length can be written as,

Substituting values we get,