Refraction and Lenses Legacy Problem #20 Guided Solution
Problem*
The converging lens on Julia's camera has a focal length of 52 mm. She uses the camera to take a picture of her friends at South's homecoming. Her friends are located a distance of 2.45 m from the camera as Julia focuses in on them. Calculate the distance from the lens to the film (i.e, the image distance).
Audio Guided Solution
One common problem which physics students have in solving physics problems is a tendency to ignore the units on given quantities. And if you're having difficulty solving this problem, that could be the source of your difficulty. In this question, we're given the focal length of a camera lens. It's 52 millimeters. And we're given the distance that an object happens to be, Julius Renz, the distance those objects are from the camera lens, 2.45 meters. And we're asked to calculate the image distance, the distance from the lens to the film that creates a focused image. So we wish to calculate d-image using the lens equation. The lens equation states that 1 over the focal length equals 1 over the object distance plus 1 over the image distance. The equation can be rearranged to solve for the image distance. It would become 1 over image distance equals 1 over focal length minus 1 over object distance. And this is where the issue of units comes in. Because you have to go 1 over 52 millimeters as the 1 over focal length minus 1 over object distance. And the object distance must be in the same set of units as the focal length. So for the 2.45 meters, it needs to be converted to millimeters using the idea that there's a thousand little millimeters in one meter. And so the 2.45 meters becomes 2,450 millimeters. And the 1 over 52 minus the 1 over 2,450 millimeters evaluates to 0.018823. And this is equal to 1 over image distance. If the reciprocal of each side is taken, you can find the image distance, and it comes out to be 53.1276 millimeters. You can round that to three significant digits, such that it's 53.1 millimeters.
Solution
53.1 mm
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities and record them in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(\descriptive{d_o}{d_o,distance object} = 24.8\unit{cm}\); \(\descriptive{d_i}{d_i,distance image} = 16.7\unit{cm}\); \(\descriptive{f}{f,focal length} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
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