/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 41 A camera lens has a focal length... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 34: Problem 41

A camera lens has a focal length of 180.0 \(\mathrm{mm}\) and an aperture diameter of 16.36 \(\mathrm{mm}\) (a) What is the \(f\) -number of the lens? (b) If the correct exposure of a certain scene is \(\frac{1}{30} \mathrm{s}\) at \(f / 11\) , what is the correct exposure at \(f / 2.8 ?\)

Short Answer

Expert verified
(a) f-number is 11.0. (b) Correct exposure at \(f/2.8\) is \(\frac{1}{480}\) s.

Step by step solution

01

Calculate f-number

The f-number (or f-stop) is given by the formula \( f/\# = \frac{f}{D} \), where \( f \) is the focal length and \( D \) is the aperture diameter. Here, \( f = 180.0 \, \text{mm} \) and \( D = 16.36 \, \text{mm} \). Substitute these values into the formula: \( f/\# = \frac{180.0}{16.36} \approx 11.0 \). Thus, the f-number of the lens is \( 11.0 \).
02

Understanding Exposure Change Rule

To determine the correct exposure at a different f-number, we use the relationship between f-stops and exposure time. Each f-stop change affects the exposure by a factor of \( 2 \). Moving from a higher f-number to a lower f-number lets in more light, therefore, faster exposure time is needed.
03

Calculate Exposure for f/2.8

Given the exposure at \( f/11 \) is \( \frac{1}{30} \) s, and wanting to determine the correct time for \( f/2.8 \), note the number of f-stops between \( f/11 \) and \( f/2.8 \). The difference in stops: \[11, 8, 5.6, 4, 2.8\] totals to 4 full f-stops decrease. Each stop is a doubling of light, thus halving the exposure time per stop. Starting from \( \frac{1}{30} \) s: \[ \frac{1}{30} \rightarrow \frac{1}{60} \rightarrow \frac{1}{120} \rightarrow \frac{1}{240} \rightarrow \frac{1}{480} \]. The correct exposure at \( f/2.8 \) is therefore \( \frac{1}{480} \) s.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Focal Length
The focal length of a camera lens is a critical aspect of how it captures images. It is the distance between the lens and the sensor when the subject is in focus. Essentially, it determines how much of the scene will be captured and how large the subjects will appear in the viewfinder or on the film/sensor.
The unit of measurement for focal length is typically millimeters (mm).
This measurement directly affects the angle of view and magnification. For example:
  • Shorter focal lengths, like 18mm, provide a wide angle of view, capturing more of the scene.
  • Longer focal lengths, such as 180mm, offer a narrow angle of view, resulting in a zoomed-in image.
Understanding focal length helps photographers choose the right lens for their needs, whether capturing vast landscapes or intimate close-ups.
F-number
The f-number, also known as the f-stop, is a measure of how wide the lens aperture opens. It is calculated using the formula:
\[ f/\# = \frac{f}{D} \]
where \( f \) is the focal length, and \( D \) is the diameter of the aperture. A smaller f-number means a larger aperture, allowing more light into the camera.
For example:
  • At \( f/2.8 \), the lens aperture is wide, admitting more light, beneficial for low light scenes.
  • At \( f/11 \), the aperture is narrower, ideal for bright conditions or achieving a larger depth of field, wherein both foreground and background are in focus.
The f-number is crucial for controlling the exposure and depth of field in photography.
Exposure Calculation
Exposure is all about how much light reaches the camera sensor and is key in capturing the desired image brightness. Photographers adjust exposure using the exposure triangle, which consists of:
  • Shutter speed
  • Aperture
  • ISO settings
In the given problem, we focus on shutter speed and aperture. Increasing aperture size (smaller f-number) lets in more light, requiring a faster shutter speed to prevent overexposure.
For an f-stop change, exposure time adjusts by a factor of two. For example, moving from \( f/11 \) to \( f/2.8 \) requires decreasing the exposure time, since more light hits the sensor with each f-stop decrease, resulting in the exposure adjustment from \( \frac{1}{30} \) s to \( \frac{1}{480} \) s.
Aperture Diameter
The aperture diameter is the physical opening in the lens that allows light to enter and reach the camera sensor. It impacts not only the exposure but also the depth of field in an image.
Aperture size is inversely related to the f-number. A larger aperture (smaller f-number) signifies a larger diameter, more light, and a shallower depth of field. Conversely, a smaller aperture (larger f-number) denotes a smaller diameter, less light, and a greater depth of field.
In practical use:
  • For portraits, a larger aperture (small f-number) provides pleasingly blurred backgrounds.
  • For landscapes, a smaller aperture (large f-number) is chosen to ensure sharp focus throughout the scene.
Understanding the role of aperture diameter aids photographers in achieving the intended visual effect and exposure level in their photos.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A double-convex thin lens has surfaces with equal radii of curvature of magnitude \(2.50 \mathrm{cm} .\) Looking through this lens, you observe that it forms an image of a very distant tree at a distance of 1.87 \(\mathrm{cm}\) from the lens. What is the index of refraction of the lens?

The left end of a long glass rod 8.00 \(\mathrm{cm}\) in diameter, with an index of refraction 1.60 , is ground and polished to a convex hemispherical surface with a radius of 4.00 \(\mathrm{cm}\) . An object in the form of an arrow 1.50 \(\mathrm{mm}\) tall, at right angles to the axis of the rod, is located on the axis 24.0 \(\mathrm{cm}\) to the left of the vertex of the convex surface. Find the position and height of the image of the arrow formed by paraxial rays incident on the convex surface. Is the image erect or inverted?

Choosing a Camera Lens. The picture size on ordinary \(35-\mathrm{mm}\) camera film is \(24 \mathrm{mm} \times 36 \mathrm{mm}\) . Focal lengths of lenses available for \(35-\mathrm{mm}\) cameras typically include \(28,35,50\) (the "normal" lens), \(85,100,135,200,\) and \(300 \mathrm{mm},\) among others. Which of these lenses should be used to photograph the following objects, assuming that the object is to fill most of the picture area? (a) a building 240 \(\mathrm{m}\) tall and 160 \(\mathrm{m}\) wide at a distance of 600 \(\mathrm{m}\) , and (b) a mobile home 9.6 \(\mathrm{m}\) in length at a distance of 40.0 \(\mathrm{m}\) .

If you run away from a plane mirror at 2.40 \(\mathrm{m} / \mathrm{s}\) , at what speed does your image move away from you?

A coin is placed next to the convex side of a thin spherical glass shell having a radius of curvature of 18.0 \(\mathrm{cm}\) . An image of the 1.5 -tall coin is formed 6.00 \(\mathrm{cm}\) behind the glass shell. Where is the coin located? Determine the size, orientation, and nature (real or virtual) of the image.
See all solutions

Recommended explanations on Physics Textbooks

Turning Points in Physics

Read Explanation

Linear Momentum

Read Explanation

Electricity

Read Explanation

Force

Read Explanation

Fields in Physics

Read Explanation

Thermodynamics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.