Question

The resolution of a digital camera is limited by two factors:

diffraction by the lens, a limit of any optical system, and the fact

that the sensor is divided into discrete pixels. Consider a typical

point-and-shoot camera that has a 20-mm-focal-length lens and

a sensor with 2.5@mm@wide pixels.

a. First,ass ume an ideal, diffractionless lens. At a distance of

100 m, what is the smallest distance, in cm, between two

point sources of light that the camera can barely resolve? In

answering this question, consider what has to happen on the

sensor to show two image points rather than one. You can use

s′ = f because s W f.

b. You can achieve the pixel-limited resolution of part a only if

the diffraction width of each image point is no greater than

1 pixel in diameter. For what lens diameter is the minimum

spot size equal to the width of a pixel? Use 600 nm for the

wavelength of light.

c. What is the f-number of the lens for the diameter you found in

part b? Your answer is a quite realistic value of the f-number

at which a camera transitions from being pixel limited to

being diffraction limited. For f-numbers smaller than this

(larger-diameter apertures), the resolution is limited by the

pixel size and does not change as you change the aperture. For

f-numbers larger than this (smaller-diameter apertures), the

resolution is limited by diffraction, and it gets worse as you

“stop down” to smaller apertures

Short answer

$$\begin{gathered} a.)m=0.00020,h=1.3cm \\ b.)D=1.2cm \\ c.)fnumber=1.66 \end{gathered}$$

Step-by-step solution

Part (a) step.1 Given information

Assume an ideal, diffractionless lens. At a distance of

100 m, what is the smallest distance, in cm, between two

point sources of light that the camera can barely resolve? In

answering this question, consider what has to happen on the

sensor to show two image points rather than one. You can use

s′ = f because s W f.

Part(a) step.2 : calculation 

Part(b) step 1:given information 

Use 600 nm for the wavelength of light.

Part (b) step 2 : simplification

Part (c) step.1 : Given information 

f-number of the lens for the diameter you found in

part b? Your answer is a quite realistic value of the f-number

at which a camera transitions from being pixel limited to

being diffraction limited. For f-numbers smaller than this

(larger-diameter apertures), the resolution is limited by the

pixel size and does not change as you change the aperture. For

f-numbers larger than this (smaller-diameter apertures), the

resolution is limited by diffraction, and it gets worse as you

“stop down” to smaller apertures

Part (c) step.2: Simplification