A camera is being used with a correct exposure at f / 4 and...

A camera is being used with a correct exposure at $f / 4$ and a shutter speed of $\frac{1}{15}$ s. In addition to the $f$ -numbers listed in Section $25.1,$ this camera has $f$ -numbers $f / 1, f / 1.4,$ and $f / 2$ . To photograph a rapidly moving subject, the shutter speed is changed to 1$/ 125$ s. Find the new $f$ -number setting needed on this camera to maintain satisfactory exposure.

Key Concepts

Aperture (f-number)

The f-number, or aperture, is a measure of the size of the lens opening that controls the amount of light entering the camera. Because the light gathered is proportional to the square of the aperture diameter, a smaller f-number (larger aperture) lets in more light, which is essential when compensating for a faster shutter speed.

Exposure Compensation

Exposure compensation involves adjusting one exposure parameter—such as aperture—when another parameter like shutter speed changes, to maintain the same overall exposure. This process is fundamental in photography when varying settings are needed to balance light exposure without altering the inherent brightness of the final image.

Exposure Triangle

The exposure triangle refers to the relationship among aperture, shutter speed, and ISO, which together determine the total amount of light reaching the camera’s sensor. Understanding this balance is critical for achieving proper exposure in a photograph regardless of lighting conditions and desired photographic effects.

Shutter Speed

Shutter speed is the duration for which the camera’s shutter remains open, allowing light to hit the sensor. It affects not only the overall brightness of an image but also the ability to freeze or blur motion, making it crucial when photographing moving subjects.

Transcript

00:01 So in this problem, we actually have a camera initially set up for f number equals 4.

00:07 And the exposure time of the camera is 1 over 15 seconds.

00:12 Now, we want to take a picture of a fast moving object.

00:16 And then for that case, we actually want to decrease the exposure time.

00:21 So what we do is we change it to 1 over 125 seconds.

00:27 So now for that case, we want to find out the f number, the final f number, all right? so let's begin.

00:34 The first thing that we need to know here is initially it was set up at correct exposure, and we want to change the f number in such a way that we are still getting the correct exposure.

00:47 So what does that mean physically? so what that means is in both of the cases, initial and final cases, the energy that is being delivered to the film of the camera, is the same, all right? sufficient energy so that you get the correct exposure.

01:06 So let's begin with that.

01:07 So the energy, let's say e1 is the initial energy, has to be equal to e2, both of the energies that are being delivered to the film.

01:20 All right? so now from the definition of the intensity, intensity i is actually the energy per unit area, per unit time.

01:34 All right.

01:35 So from here we can actually rearrange and write for the equation here for this e1 equals e2.

01:42 We can write this down.

01:44 This is going to be i1 times a times t1 equals i2 times a times t2...

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