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A camera lens has a focal length of 180.0 mm and an aperture diameter of 16.36 mm. (a) What is the f-number of the lens? (b) If the correct exposure of a certain scene is 130s at f/11, what is the correct exposure at f/2.8?

Short Answer

Expert verified
(a) The f-number is 11. (b) The correct exposure at f/2.8 is approximately 0.5 seconds.

Step by step solution

01

Understand the f-Number Formula

The f-number, often denoted as f/ or N, is calculated using the formula N=fD, where f is the focal length of the lens, and D is the aperture diameter.
02

Calculate the f-Number

Using the given focal length f=180.0 mm and aperture diameter D=16.36 mm, we apply the formula: N=180.016.3611.00. Thus, the f-number is approximately 11.
03

Understand Exposure Relation

The exposure time needed for a lens is related to the square of the f-number, given a constant amount of light, by the formula t2=t1(N2N1)2. This formula helps us find the new exposure time given a different f-number.
04

Calculate New Exposure Time

We're given t1=130 seconds at f/11, and we need to find t2 at f/2.8. Using the formula: t2=130(112.8)2130×15.4912. Thus, the correct exposure at f/2.8 is approximately 0.5 seconds.

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Key Concepts

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

Focal Length
In the world of camera optics, understanding focal length is essential. Focal length is the distance between the lens and the image sensor when the subject is in focus. It is usually measured in millimeters (mm). This length determines the field of view and magnification of the image.

A longer focal length results in a narrower field of view, making it easier to zoom in on distant subjects. Conversely, a shorter focal length offers a wider view, suitable for capturing vast landscapes. Using a lens with a focal length of 180.0 mm, for instance, means that it's likely geared toward zoomed-in shots or portraits where the background is less emphasized.
Aperture
Aperture refers to the size of the opening in the lens through which light enters. This opening can be adjusted, much like the pupil of an eye. A larger aperture allows more light to reach the camera sensor.

Aperture size is typically expressed in terms of the diameter of the aperture opening, measured in millimeters. In the given example, the lens has an aperture diameter of 16.36 mm. This indicates how wide the lens opening is, impacting the brightness of the captured image. A larger aperture not only increases light intake but also affects the depth of field, enabling beautifully blurred backgrounds, which is especially popular in portrait photography.
Exposure Time
Exposure time, sometimes known as shutter speed, is the duration for which the camera's sensor is exposed to light. It is crucial in determining the overall brightness of the photo. Shorter exposure times freeze motion, while longer times can capture motion blur.

In our exercise, the initial exposure time is 130 seconds. Adjustment of exposure time is necessary when changing the f-number of the lens.Using a mathematical relationship involving the square of the f-number, we can compute the new exposure time required when the aperture size is altered to maintain consistent illumination.
f-number
The f-number, also known as the f-stop, is a critical concept in optics that influences both exposure and depth of field. It is calculated by dividing the focal length by the aperture diameter, represented as N=fD.

A smaller f-number (e.g., f/2.8) means a larger aperture and more light entering the camera. This is ideal for shooting in low-light conditions. On the other hand, a larger f-number (e.g., f/11) denotes a smaller aperture, suitable for brightly lit scenes.

In practical terms, understanding the f-number helps photographers adjust exposure settings correctly, as demonstrated in our exercise's calculations. Switching from an f/11 to an f/2.8 aperture requires recalculating the exposure time to ensure the photographed scene remains properly exposed.

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Most popular questions from this chapter

The cornea behaves as a thin lens of focal length approximately 1.8 cm, although this varies a bit. The material of which it is made has an index of refraction of 1.38, and its front surface is convex, with a radius of curvature of 5.0 mm. (a) If this focal length is in air, what is the radius of curvature of the back side of the cornea? (b) The closest distance at which a typical person can focus on an object (called the near point) is about 25 cm, although this varies considerably with age. Where would the cornea focus the image of an 8.0-mm-tall object at the near point? (c) What is the height of the image in part (b)? Is this image real or virtual? Is it erect or inverted? (Note: The results obtained here are not strictly accurate because, on one side, the cornea has a fluid with a refractive index different from that of air.)

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A camera with a 90-mm-focal-length lens is focused on an object 1.30 m from the lens. To refocus on an object 6.50 m from the lens, by how much must the distance between the lens and the sensor be changed? To refocus on the more distant object, is the lens moved toward or away from the sensor?

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