# Name: Date: Math in Special Effects: Try Other Challenges. Answer Key

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1 Name: Date: Math in Special Effects: Try Other Challenges When filming special effects, a high-speed photographer needs to control the duration and impact of light by adjusting a number of settings, including frame rate, shutter angle, and f- stop. Knowing the relationship between these variables can help you figure out how to get the best shot. Your challenge is to learn how a camera setting, called an, affects the amount of light coming through the lens and use your understanding of it to improve your shot. This activity is designed to be used in conjunction with the online interactive. Go to click on The Challenges, then scroll down and click on Math in Special Effects: Try other challenges. A. SELECT A LENS SIZE 35 mm 50 mm 200 mm B. RECORD F-STOP SETTINGS 1. Identify what you already know. Look at the chart that corresponds to the lens you selected (on the last page of this handout). View Photo Fundamentals for definitions. The two sets of data displayed in the chart are: Focal length and Following the instructions in the interactive, record the value that corresponds to the fixed and the for each row in the chart. (Note: s are rounded to the tenth.) C. HOW ARE FOCAL LENGTH, APERTURE, AND F-STOP RELATED? 1. Plan it out. Describe your strategy for identifying the relationship represented by the f- stop in terms of and the. Students should examine the data and look for a pattern. They may notice that the is a ratio of the to the the. 2. Model your data by identifying an equation you think best represents the relationship. Explain your reasoning as to why you chose this equation. s =

2 3. Solve for the variables using the equation you selected and your recorded data. Show all work below. Be sure to record the corresponding values in your chart to test out your prediction. 4. Validate your answer: Is your equation a good representation of the relationship? If not, try looking for a pattern to determine how to find the matching and try another equation. If so, explain how the diameter and are related. There is an inverse relationship between and the. D. HOW MUCH LIGHT PASSES THROUGH AT A GIVEN F-STOP? 1. Plan it out. Identify the formula you will use for calculating the area, A, of the opening for each. 2. Solve by calculating A for each row in your chart. (Use = 3.14 and round to the sq mm for 200mm lens or the tenth for 50mm or 35mm lens.) Use the space below to show your work. Record your solutions in each row of the chart. E. IDENTIFY THE RELATIONSHIP BETWEEN F-STOP AND AREA OF APERTURE 1. Plan it out. Describe your strategy for identifying the relationship between and. Students should examine the data to look for a pattern. They may notice that there is a relationship between s and light intensity (or area of the ). Opening up to the next lower (for instance, going from f/1.4 to f/1) lets in twice as much light by increasing the the opening by a factor of, or about As diameter increases by a factor of, the area of the, and therefore, light intensity, doubles. Conversely, closing down to each greater (for instance, going from f/2 to f/2.8) reduces the light intensity by half. 2. Model your data by identifying an equation you think best represents the relationship. Why did you choose this equation? A = 3. Solve for the constant, k, for each row. Show all work below. Be sure to record the values for in your chart to test out your prediction. (Round to the thousand.) 2

3 4. Validate your answer: Is your equation a good representation of the relationship? If not, try looking for a pattern to determine how to find the constant value and try another equation. If so, explain how the and the are related. There is an inverse square relationship between and the. F. USE YOUR UNDERSTANDING OF F-STOPS TO ADJUST THIS SHOT 1. The is currently set at f/5.6, but the shot is underexposed. If the shot requires a setting that is 8 times brighter, to what should you adjust to get more light? Open up 3 stops to f/2 2. If the shot requires a setting that is 1/4 as bright and the is currently set at f/5.6, to what should you adjust to get less light? Close down 2 stops to f/11 3. If the shot requires a setting that is 8 times brighter and the is currently set at f/16, to what should you adjust to get more light? Open up 3 stops to f/ Explain your reasoning. If you were going to a friend to explain your strategy for finding the correct for any shot, what would you tell them? There is a relationship between s and light intensity (or area of the ). Opening up to the next lower lets in twice as much light by increasing the the opening by a factor of, or about As diameter increases by a factor of, the area of the, and therefore, light intensity, doubles. Conversely, closing down to each greater reduces the light intensity by half. 3

4 Photo Fundamentals Aperture Diameter of An opening in the lens, or circular hole, that can vary in size. It is adjusted to increase or decrease the amount of light. The physical size of the hole measured through its center point. Half of the diameter is the radius of the lens. The measurement, in square mm, of the opening of the hole formed by the. Focal length The distance between the optical center of the lens (typically, where the is located) and the image plane, when the lens is focused at infinity. Image plane The fixed area behind a camera lens inside the camera at which the sensor or film is located, and on which pictures are focused. The camera setting that regulates how much light is allowed by changing the size, which is the opening of the lens. Solutions for 35 mm lens 35 mm lens , , , , , , ,000 4

5 Solutions for 50 mm lens 50 mm lens , , , , , , , , ,000 Solutions for 200 mm lens 200 mm lens integer) ,400 31, ,030 31, ,850 31, ,002 31, ,963 31, ,000 31, ,000 5

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