Focal Lengths of Two Lenses of a Microscope

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A microscope is made in a tube 25.0 cm long. It magnifies 5.00 x 102 times, 50.0 times by the objective lens and 10.0 times by the eyepiece. What are the focal lengths of the two lenses?

 

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What have you done so far?

 

[Moetasim]

Based on the given information, we can calculate the focal lengths of the two lenses using the formula for magnification (M = -d_i/d_o, where M is the magnification, d_i is the distance between the object and the lens, and d_o is the distance between the lens and the image).

For the objective lens, we can set M = 50.0 and d_i = 25.0 cm (since the length of the microscope tube is 25.0 cm). Solving for d_o, we get d_o = -1.25 cm. Since the focal length (f) is equal to half of the distance between the lens and the image (f = d_o/2), the focal length of the objective lens is 0.625 cm or 6.25 mm.

For the eyepiece lens, we can set M = 10.0 and d_i = -1.25 cm (since the image from the objective lens is the object for the eyepiece lens). Solving for d_o, we get d_o = -12.5 cm. Therefore, the focal length of the eyepiece lens is 6.25 cm or 62.5 mm.

In summary, the focal length of the objective lens is 6.25 mm and the focal length of the eyepiece lens is 62.5 mm. These values are important in determining the magnification and resolution of the microscope, as well as the distance between the lenses for proper functioning.