An f / 2.80 CCD camera has a 105-mm focal length lens and can focus on objects from infinity to

An f / 2.80 CCD camera has a 105-mm focal length lens and...

An $f / 2.80$ CCD camera has a $105-\mathrm{mm}$ focal length lens and can focus on objects from infinity to as near as 30.0 $\mathrm{cm}$ from the lens. (a) Determine the camera's aperture diameter. Determine the (b) minimum and (c) maximum distances from the CCD sensor over which the lens must be able to travel during focusing. Note: "f/2.80" means "an $f$ -number of 2.80 ."

Key Concepts

Focusing Mechanism

A focusing mechanism adjusts the position of the lens elements relative to the image sensor to obtain a sharp image of objects at different distances. Understanding how changes in object distance require adjustments in the image distance—via the thin lens equation—is crucial in determining the range over which the lens must travel during focusing from close subjects to infinity.

Thin Lens Equation

The thin lens equation, expressed as 1/object distance + 1/image distance = 1/focal length, is a cornerstone of geometric optics. It relates the focal length of the lens to the distances from the object to the lens and from the lens to the image sensor. This equation is essential for calculating how the lens must be positioned relative to the sensor to focus on objects at various distances.

Aperture Diameter

The aperture diameter is the physical size of the opening in the lens through which light passes. It is directly computed by dividing the focal length by the f-number. This concept is fundamental in optics as it affects both the brightness of the image and the depth of field, determining the overall performance of the lens system.

F-number

An f-number is defined as the ratio of the lens's focal length to the diameter of the entrance pupil (aperture). It is a key parameter in optics because it not only determines the amount of light entering the system but also influences the depth of field and exposure settings. A lower f-number, such as 2.80, indicates a wider aperture that allows more light to pass through.

Transcript

00:01 So in this problem, we have a ccd camera, which has a focal length of 105 millimeter, and f number equals 2 .8.

00:10 So we also know that the camera can focus an object from infinity down to 30 centimeter.

00:20 So what that means is the object distance can be p1 equals infinity down to p2 equals 300 millimeter.

00:28 So to solve the problem a, which is to find the diameter of the aperture of the lens, all we need to do is just use the definition of f number.

00:43 So let's do that.

00:47 So the definition of the f number is the ratio between the focal length of the lens and the diameter of the aperture, right? so from here the diameter of the aperture d is f over f number which is 105 millimeter over 2 .8.

01:17 This is going to give us 37 .5 millimeter.

01:24 So this is the diameter of the aperture.

01:30 All right.

01:31 So let's go to part b.

01:33 In part b, we want to find out the minimum distance between the lens and the cctv sensor.

01:40 Remember, that is also the image distance.

01:44 So that's what matters.

01:45 So to find the minimum distance, we have to assume that the object is at infinity.

01:52 All right.

01:53 So for part b, we are actually going to use object distance at infinity, which is p1 equals infinity...