Compound Microscope: Calculating Focal Length of Objective

[kmj9k]

1. A compound microscope has the objective and eyepiece mounted in a tube that is 18.0 cm long. The focal length of the eyepiece is 2.24 cm, and the near-point distance of the person using the microscope is 25.0 cm. If the person can view the image produced by the microscope with a completely relaxed eye, and the magnification is -4150, what is the focal length of the objective? (Include the sign.)



2. M= (-di / f of objective) (N / f eyepiece)



3. di = 18 - f objective - f eyepiece = 18-2.24- f obj = 15.76- fobjective
4150 = - ( (15.76- fobjective) / f objective) (25.0/2.24)
solved for f objective, and got -0.424 mm, but that's wrong.

 

[anathema]

[/b]

Hello there,

I would like to clarify a few things about your calculations. First, the negative sign in the magnification formula indicates that the image produced by the microscope is inverted. Therefore, we should use a positive value for the magnification (-4150) in our calculations.

Secondly, the formula you used (M= (-di / f of objective) (N / f eyepiece)) is incorrect. The correct formula for magnification in a compound microscope is M = (-di / do) (N / f), where di is the distance of the image from the eyepiece, do is the distance of the object from the objective, N is the near-point distance, and f is the focal length of the eyepiece.

Using this formula, we can rearrange to solve for the focal length of the objective: do = (-M / N) f. Plugging in the given values, we get do = (-(-4150) / 25.0) (2.24) = 334.4 mm.

Therefore, the focal length of the objective is approximately 334.4 mm. I hope this helps clarify any confusion. Keep up the good work on your calculations!

 

[m2003]

I would first check the calculations to ensure they are accurate. If the calculations are correct, then I would consider other factors that may be affecting the results. For example, the precision of the measurements, the condition of the microscope, and the accuracy of the magnification value provided. I would also check if there are any other variables that may affect the focal length of the objective, such as the distance between the objective and the eyepiece. If all these factors have been accounted for, and the calculated focal length is still incorrect, then it is possible that there is an error in the given information or in the assumptions made in the calculations. In this case, it may be necessary to repeat the experiment or seek additional information to accurately determine the focal length of the objective.