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A camera has a thin lens with an aperture of \(8 \mathrm{~mm}\) and a focal length of \(10 \mathrm{~cm}\). What is the [f / (number)] of the system if a stop \(7 \mathrm{~mm}\) in diameter is mounted \(5 \mathrm{~mm}\) in front of the lens? If it is mounted \(5 \mathrm{~mm}\) behind the lens?

Short Answer

Expert verified
In both cases, the f/number for the system is approximately 14.29.

Step by step solution

01

Understand the formula for f/number

The f/number, often represented as N, is a dimensionless value that represents the ratio between the focal length (f) and the diameter of the aperture (D). The formula for f/number is given as: \(N=\frac{f}{D}\) In the given problem, we know the focal length (f) of the lens is \(10 cm\) and the lens's aperture (D) is \(8 mm\).
02

Evaluate the effective aperture diameter

For both cases, we are given a stop with a diameter of \(7 mm\). Case 1: Stop mounted \(5 mm\) in front of the lens. In this case, the effective aperture diameter (D') is given by the stop diameter, which is \(7 mm\). Case 2: Stop mounted \(5 mm\) behind the lens. In this case, as well, the effective aperture diameter (D') is given by the stop diameter, which is \(7 mm\). Now, we can use these effective aperture diameters, in both cases, to calculate the f/number.
03

Calculate the f/number

Case 1: Stop mounted \(5 mm\) in front of the lens. We have focal length (f) = \(10 cm\) and effective aperture diameter (D') = \(7 mm\). Using the formula for f/number \(N = \frac{f}{D'}\), we get: \(N =\frac{10 cm}{7 mm} = \frac{10}{0.7} = 14.29\). Thus, the f/number for the system in this case is approximately 14.29. Case 2: Stop mounted \(5 mm\) behind the lens. We have focal length (f) = \(10 cm\) and effective aperture diameter (D') = \(7 mm\). Using the formula for f/number \(N = \frac{f}{D'}\), we get: \(N = \frac{10 cm}{7 mm} = \frac{10}{0.7} = 14.29\). Thus, the f/number for the system in this case is also approximately 14.29.

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Key Concepts

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

Aperture
Aperture refers to the opening in a lens through which light passes to enter the camera. It's analogous to the pupil of your eye, widening or narrowing to control the amount of light that hits the retina. In photography, the aperture size is a critical setting that affects exposure, depth of field, and the overall composition of an image. A larger aperture (smaller f/number) allows more light to pass through, which is beneficial in low light conditions, whereas a smaller aperture (larger f/number) lets in less light but provides a greater depth of field, bringing more of the scene into focus.

For students learning about aperture, it's vital to grasp its influence on image brightness and sharpness. Adjusting the aperture size can significantly alter the appearance of a photograph, making it a powerful tool in the art of visual storytelling.
Focal Length
Focal length is the distance between the lens and the image sensor when the subject is in focus, usually stated in millimeters (mm). It determines the lens's angle of view; in other words, how much of the scene will be captured and how large individual elements will be in the frame. Shorter focal lengths provide a wider field of view and are often used for landscapes, while longer focal lengths offer a narrower view, magnifying distant objects such as in wildlife photography.

When explaining focal length to students, it's important to relate it to the practical aspects of photography. For instance, using a lens with a longer focal length can bring objects closer, which is beneficial for taking sports or action photographs. Conversely, using a shorter focal length will fit more into the frame, which is ideal for architectural or street photography.
Thin Lens
A thin lens is a lens with a thickness that is small compared to its focal length, often used in simple optical systems models. Thin lenses are ideal for education as they simplify the study of optics by reducing the complexity involved in light refraction. In thin lens theory, light is assumed to refract at the lens's central plane, allowing for straightforward calculations of image and object relationships using the lens formula.

When acquainting students with the concept of the thin lens, it's beneficial to emphasize its uses in various devices, such as cameras, microscopes, and eyeglasses. This connection to familiar objects can make the abstract concept more tangible and understandable.
Optics
Optics is a branch of physics that deals with the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics encompasses both the study of light's properties and its practical applications such as lenses, telescopes, microscopes, and cameras.

When teaching the essentials of optics to students, one effective method is to discuss how light travels and how it is manipulated by different materials to create images. For example, a converging lens in a camera focuses light rays to form a sharp image on the film or sensor. Understanding optics is crucial for anyone interested in photography, as it lays the foundation for concepts like focus, exposure, and the creation of images.
Dimensionless Value
A dimensionless value, also known as a unitless value, is a pure number without any physical units attached to it. It provides a way to compare different quantities and often emerges as a ratio of two like-dimensioned quantities, canceling the units out. In photography, the f/number or f-stop is a dimensionless value derived from the ratio of the lens' focal length to the diameter of the aperture.

It's essential when discussing dimensionless values to point out their significance in standardizing measurements, making comparisons, and understanding relationships in formulas. For instance, the f/number is used to quantify the amount of light that passes through a lens, allowing photographers to communicate and adjust settings consistently across various camera systems.

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Most popular questions from this chapter

A distant object is observed through a telescope consisting of an objective lens of focal length \(30 \mathrm{~cm}\) and a single eyepiece lens of focal length \(5 \mathrm{~cm}\). The telescope is adjusted so that the final image observed by the eye is \(40 \mathrm{~cm}\) from the eye lens. a) Find the distance between the two lenses. b) Make a careful diagram tracing a ray bundle from a lateral point on the object to the retina. c) Calculate the magnifying power of this arrangement.

What should be the widest and the least spacing of a set of single slits in the image plane, suitable for testing, by transfer function, of a telescope of \(10 \mathrm{x}\) angular magnification, aimed at a target \(5 \mathrm{~km}\) away, consisting of bars varying in width from \(6 \mathrm{~cm}\) to \(10 \mathrm{~cm}\) ? Assume image distance of \(10 \mathrm{~cm}\) and the wavelength of light used is \(5000 \mathrm{~A}^{\circ}\)

An astronomical telescope, consisting of an objective lens of \(+40 \mathrm{~cm}\) focal length and an eyepiece of \(+2.5 \mathrm{~cm}\) focal length, is focused for visual observation at the distance of most distinct vision, on a scale \(3 \mathrm{~m}\) away. 1) What is the length of the telescope (distance between the lenses)? 2) What is the total linear lateral magnification?

A crude telescope is constructed of two spectacle lenses of focal lengths \(100 \mathrm{~cm}\) and \(20 \mathrm{~cm}\) respectively, a) Find its angular magnification. b) Find the height of the image formed by the objective of a building \(200 \mathrm{ft}\) high and one mile distant.

An eyepiece is made of two thin lenses, each of \(20 \mathrm{~mm}\) focal length, separated by a distance of \(16 \mathrm{~mm}\). Find: (a) the equivalent focal length of the eyepiece, (b) the distance of the focal plane from the nearer lens, and (c) the angular magnification provided.

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