Refraction and Lenses Legacy Problem #24 Guided Solution
Problem*
In an effort to read the miniaturized writing in Khaled's lab notebook, Mr. H pulls a magnifying glass from his drawer. He places the magnifying glass a distance of 6.3 cm from the paper and produces an upright image of the writing which is magnified by a factor of 4.8. Determine the focal length of the lens used by the magnifying glass.
Audio Guided Solution
In this question, the text within a lab notebook is attempting to be read using a magnifying glass. The text becomes the object, and the object distance is equal to 6.3 centimeters. The magnifying glass is a lens, which creates a magnified and upright image of the text, and it's magnified by a factor of 4.8. So I can say that m, for magnification, equal positive 4.8. We're asked to determine the focal length, f, is my unknown quantity. To find the focal length, I need to know two things, object distance and image distance. The object distance is already given, 6.3 centimeters. I need to find the image distance first, and to do so, I need to use the fact that the magnification is positive 4.8. So the magnification is the high to whole ratio, but it's also equal to the negative die per doe ratio. So 4.8 is equal to die, the image distance, divided by doe, 6.3 centimeters, with a negative sign in front. I can rearrange and solve for die, and 4.8 times the negative 6.3 comes out to be negative 30.24 centimeters. Now that I know the value of die, I can use the lens equation to find the focal length. I see that 1 over f equal 1 divided by 6.3, plus 1 divided by negative 30.24. I evaluate the right side of this equation, and it comes out to be 0.12566. That's not equal to the focal length. That's 1 over the focal length. If I take the reciprocal of this number, I get the focal length, and it comes out to be 7.9579 centimeters, and I can round that to two significant digits, 8.0 centimeters.
Solution
8.0 cm
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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