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Chapter 27: Problem 6

Four camera lenses have the following focal lengths and \(f\) -numbers: $$ \begin{array}{lcc} \hline \text { Lens } & \text { Focal length }(\mathrm{mm}) & \text { f-number } \\ \hline \mathrm{A} & 150 & f / 1.2 \\ \mathrm{B} & 150 & f / 5.6 \\ \mathrm{C} & 35 & f / 1.2 \\ \mathrm{D} & 35 & f / 5.6 \\ \hline \end{array} $$ Rank these lenses in order of increasing aperture diameter. Indicate ties where appropriate.

Short Answer

Expert verified
D, B, C, A

Step by step solution

01

Formula for Aperture Diameter

To find the aperture diameter of a camera lens, use the formula \( D = \frac{F}{N} \), where \( D \) is the aperture diameter, \( F \) is the focal length, and \( N \) is the f-number.
02

Calculate Aperture for Lens A

For Lens A, with a focal length of 150 mm and an f-number of 1.2, the aperture diameter is \( D = \frac{150}{1.2} = 125 \text{ mm} \).
03

Calculate Aperture for Lens B

For Lens B, with a focal length of 150 mm and an f-number of 5.6, the aperture diameter is \( D = \frac{150}{5.6} \approx 26.79 \text{ mm} \).
04

Calculate Aperture for Lens C

For Lens C, with a focal length of 35 mm and an f-number of 1.2, the aperture diameter is \( D = \frac{35}{1.2} \approx 29.17 \text{ mm} \).
05

Calculate Aperture for Lens D

For Lens D, with a focal length of 35 mm and an f-number of 5.6, the aperture diameter is \( D = \frac{35}{5.6} \approx 6.25 \text{ mm} \).
06

Rank the Lenses

Order the lenses by increasing aperture diameter: Lens D (6.25 mm), Lens B (26.79 mm), Lens C (29.17 mm), and Lens A (125 mm).

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Key Concepts

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

Focal Length
Focal length is fundamental to understanding camera lenses. It defines how much of a scene the lens can capture. The focal length of a lens is the distance between the lens and the image sensor when the subject is in focus. It is measured in millimeters (mm). The longer the focal length, the narrower the field of view. This is why telephoto lenses, which have long focal lengths, are used to zoom in on distant subjects. Conversely, lenses with short focal lengths capture a wider scene, which is ideal for landscapes or architectural photography. In our exercise, lenses A and B have a focal length of 150mm, making them telephoto lenses. Lenses C and D have a focal length of 35mm, classifying them as wide-angle lenses, capturing a larger area in the frame.
f-number
The f-number, also known as the f-stop, indicates the size of the lens aperture. It's expressed as a ratio of the focal length to the diameter of the aperture (opening) allowing light to enter. Lower f-numbers (e.g., f/1.2) mean a larger aperture, which lets in more light. This is beneficial for low-light conditions and achieving a shallow depth of field. Higher f-numbers (e.g., f/5.6) depict a smaller aperture, which allows less light into the camera and results in a greater depth of field, often used in landscape photography. In the exercise, the f-number helps to determine the aperture diameter using the formula \( D = \frac{F}{N} \), where \( D \) is the aperture diameter, \( F \) is the focal length, and \( N \) is the f-number.
Camera Lenses
Camera lenses are an integral part of photography. They determine how a camera captures light and forms an image. Lenses are made of multiple pieces of glass or other materials inside a framework. They can vary widely in their design, based on their intended use and the photographic needs they fulfill. - **Wide-Angle Lenses:** These have shorter focal lengths, capturing broader scenes. Great for landscapes. - **Telephoto Lenses:** With longer focal lengths, these lenses zoom in on distant subjects and are fantastic for wildlife or sports photography. - **Prime Lenses:** These lenses have a fixed focal length and generally provide sharper images than zoom lenses. Understanding both the focal length and the f-number is essential when selecting a lens. Choices affect the field of view, the amount of light captured, and the depth of field in photographs. In our example, the focus was on determining aperture diameter, directly influencing how much light the lens can gather.

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Most popular questions from this chapter

The focal length of the human eye is approximately \(1.7 \mathrm{cm} .\) (a) What is the \(f\) -number for the human eye in bright light, when the pupil diameter is \(2.0 \mathrm{mm} ?\) (b) What is the \(f\) -number in dim light, when the pupil diameter has expanded to \(7.0 \mathrm{mm} ?\)

You are comfortably reading a book at a distance of \(24 \mathrm{cm}\). (a) What is the refractive power of your eyes? (b) Does the refractive power of your eyes increase or decrease when you move the book farther away? Explain. (For the purposes of this problem, treat the eye as a single-lens system, with the retina \(2.40 \mathrm{cm}\) from the lens.)

A Big Eye The largest eye ever to exist on Earth belonged to an extinct species of ichthyosaur, Temmodontosaurus platyodon. This creature had an eye that was \(26.4 \mathrm{cm}\) in diame ter. It is estimated that this ichthyosaur also had a relatively large pupil, giving it an effective aperture setting of about \(f / 1.1\). (a) Assuming its pupil was one-third the diameter of the eye, what was the approximate focal length of the ichthyosaur's eye? (b) When the ichthyosaur narrowed its pupil in bright light, did its \(f\) -number increase or decrease? Explain.

The Hale Telescope The 200-in. (5.08-m) diameter mirror of the Hale telescope on Mount Palomar has a focal length \(f=16.9 \mathrm{m}\) (a) When the detector is placed at the focal point of the mirror (the "prime focus"), what is the \(f\) -ratio for this telescope? (b) The coude focus arrangement uses additional mirrors to bend the light path and increase the effective focal length to \(155.4 \mathrm{m} .\) What is the \(f\) -ratio of the telescope when the coude focus is being used? (Coude is French for "elbow," since the light path is "bent like an elbow." This arrangement is useful when the light needs to be focused onto a distant instrument.)

Octopus Eyes To focus its eyes, an octopus does not change the shape of its lens, as is the case in humans. Instead, an octopus moves its rigid lens back and forth, as in a camera. This changes the distance from the lens to the retina and brings an object into focus. (a) If an object moves closer to an octopus, must the octopus move its lens closer to or farther from its retina to keep the object in focus? (b) Choose the best explanation from among the following: I. The lens must move closer to the retina-that is, farther away from the object-to compensate for the object moving closer to the eye. II. When the object moves closer to the eye, the image produced by the lens will be farther behind the lens; therefore, the lens must move farther from the retina.
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