Sharper Image : A Lesson by Mathalicious

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It can be incredibly frustrating to snap what you think is a great picture, only to have it come out blurry. Of course it helps to have a steady hand, but there’s electronic help available if you’re willing to cough up some extra cash for a lens with vibration reduction.

In this lesson, students interpret graphs and use right triangle trigonometry to explore the relationship between focal length, viewing angle, and blurriness. In the end, they figure out when vibration reduction might help them take clearer pictures, and when it might not be worth the cost.

Students will

Use right triangle trigonometry to calculate unknown distances from a diagram
Write general expressions to describe a lens’s vertical coverage of an object in terms of its viewing angle and the camera’s distance from the subject
Calculate absolute and relative error for a camera that moves while taking a picture
Interpret graphs describing how a lens’s viewing angle and relative error are related to its focal length
Develop questions to help someone decide under what circumstances it might make sense to purchase vibration reduction in a lens

Before you begin

Students should be familiar with the basic definitions of the trigonometric ratios, and be able to write expressions involving the relationships among the sides and angles of a right triangle.