Refraction and Lenses Legacy Problem #26 Guided Solution
Problem*
A lens produces a virtual image located 33.8 cm from the lens when the object is located 18.5 cm from the lens. Determine the focal length of the lens. What kind of lens is it?
Audio Guided Solution
In this question we're told that a virtual image is being created and it's a distance of 33.8 cm from the lens. This gives me information about DI or D-image. I say D-image equal negative 33.8 cm. The negative is the characteristic of a virtual image. Virtual images have negative image distances. This is true when the object distance is located 18.5 cm from the lens. So D-object is 18.5 cm. They ask me what the focal length of the lens is and what kind of lens it is. So to find the focal length I simply use the lens equation. The hard work has been done. I've determined the DI value, which is negative, and the DO value. So I say 1 over F is equal to 1 over 18.5 plus 1 over the negative 33.8. I evaluate the right side of the equation. It comes out to be 0.024468. I take the reciprocal of that and it gives me the focal length. The focal length is 40.8693 cm. I can round that to three significant digits, 40.9 cm. The fact that the focal length came out to be positive is an indicator to me that this lens must be a converging lens. I also know that it must be a converging lens because diverging lenses, when they produce virtual images, which they always do, always produce them with an image distance that is less than the object distance. And here in this case the image distance is greater than the object distance. So that's another reason I know this must be a converging lens.
Solution
f = 40.9 cm
Lens type: converging
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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