You are trying to construct a compoundmicroscope given two lenses with focal length1.0 cm and 4.0 cm. How far apart should youplace the lenses in order to obtain an angularmagnification of 60?(A) 9.6 cm(B) 14.6 cm(C) 12.3 cm(D) 18.2 cm
Question
You are trying to construct a compoundmicroscope given two lenses with focal length1.0 cm and 4.0 cm. How far apart should youplace the lenses in order to obtain an angularmagnification of 60?(A) 9.6 cm(B) 14.6 cm(C) 12.3 cm(D) 18.2 cm
Solution
The angular magnification (M) of a compound microscope is given by the formula:
M = -D * f_o / f_e
where:
- D is the near point (usually taken as 25 cm for a normal eye),
- f_o is the focal length of the objective lens, and
- f_e is the focal length of the eyepiece lens.
Given that the magnification is 60, the focal length of the objective lens (f_o) is 1.0 cm, and the focal length of the eyepiece lens (f_e) is 4.0 cm, we can substitute these values into the formula:
60 = -25 cm * 1.0 cm / 4.0 cm
Solving for D, we get D = -60 * 4.0 cm / 1.0 cm = -240 cm. The negative sign indicates that the image is inverted.
The distance between the lenses (d) is given by the formula:
d = f_o + f_e - D
Substituting the given values:
d = 1.0 cm + 4.0 cm - (-240 cm) = 245 cm
So, the lenses should be placed 245 cm apart. However, none of the given options (A: 9.6 cm, B: 14.6 cm, C: 12.3 cm, D: 18.2 cm) match this result. There might be a mistake in the problem or the provided options.
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