Problem 35 - Physics for Scientists and Engineers with Modern Physics

Question

(I) A television camera lens has a 17 -cm focal length and a lens diameter of \(6.0 \mathrm{~cm}\). What is its \(f\) -number?

Step-by-Step Solution

Answer

The f-number of the lens is approximately 2.83.

Step 1: Understand the Problem

We need to calculate the f-number of a camera lens. The f-number can be found by dividing the focal length of the lens by the diameter of the lens aperture. The formula is:\[ f\text{-number} = \frac{\text{focal length}}{\text{aperture diameter}} \]

Step 2: Apply the Given Values

Substitute the given values in the problem into the formula. The focal length is given as 17 cm, and the aperture diameter is 6.0 cm. Thus, we have:\[ f\text{-number} = \frac{17\text{ cm}}{6.0\text{ cm}} \]

Step 3: Calculate the F-number

Perform the division using the substituted values to find the f-number.\[ f\text{-number} = \frac{17}{6.0} \approx 2.83 \]

Step 4: Interpret the Result

The f-number, also known as the f-stop, describes the aperture diameter relative to the focal length. An f-number of approximately 2.83 means this lens has good light-gathering ability for its size.

Key Concepts

Focal Length

The focal length of a lens is a crucial concept in understanding optics and photography. It is the distance between the lens and the image sensor, where the image is brought into focus. In simple terms, it determines how "zoomed in" or "wide" a scene appears when viewed through the lens.
Think of focal length as the lens’s ability to bring distant objects into clear view.

• A shorter focal length (e.g., 18mm, 35mm) captures a wider field of view, often used in landscape photography to show more of the scene.
• A longer focal length (e.g., 100mm, 200mm) results in a narrower field of view, suitable for capturing details in distant subjects, such as wildlife or sports photography.

In our exercise, the camera lens has a focal length of 17 cm. This value sets the stage for how much of the scene can be captured and at what magnification the objects appear. Understanding the focal length helps in predicting how the lens will behave in various photography scenarios.

Aperture Diameter

The aperture diameter is an essential feature of a camera lens that affects both the exposure and depth of field in an image. The aperture is an opening in the lens that allows light to pass through to the camera sensor.
This diameter directly impacts the f-number, which in turn influences the brightness and sharpness of the captured image.

• A larger aperture (smaller f-number) allows more light to enter, which is beneficial for low-light conditions.
• A smaller aperture (larger f-number) restricts light entry and is often used in bright conditions or to achieve a greater depth of field.

In our exercise, the aperture diameter is 6.0 cm. This measurement, together with the focal length, determines the f-number, guiding you in understanding the lens's ability to gather light effectively. Adjusting the aperture size is key in photography to balance light exposure and focus.

Lens Optics

Lens optics is the science and technology behind the design and function of camera lenses. These optics encompass elements like focal length, aperture, and various lens components working together to focus light precisely onto the camera sensor.
The quality of lens optics affects image clarity, color accuracy, and distortion.

Key Aspects of Lens Optics:

• Lens Elements: Multiple glass components inside the lens that work to bend and focus light onto the sensor.
• Coatings: Special coatings on these glass elements enhance light transmission and reduce lens flares and reflections.
• Stabilization: Some lenses have built-in stabilization to counteract hand movements for sharper images.

A good understanding of lens optics is vital for capturing high-quality images. This understanding allows photographers to select lenses that best cater to their shooting requirements, based on the scene's demands and lighting conditions.