Finding the Position of a Sample Using Microscope Magnification

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SUMMARY

The discussion centers on calculating the position of a sample in relation to a microscope with a tube length of 200 mm, achieving a total magnification of 800× using a 40× objective lens and a 20× eyepiece. The participant calculated the focal lengths of the objective and eyepiece lenses to be 0.025 m and 0.05 m, respectively. Despite determining the virtual image position and attempting to find the sample's distance from the objective lens, the participant received incorrect feedback from Mastering Physics. The final calculated distance was 2.97 cm, which was not accepted as correct.

PREREQUISITES
  • Understanding of microscope optics, specifically total magnification calculations.
  • Familiarity with the lens formula: 1/s + 1/s' = 1/f.
  • Knowledge of focal lengths for objective and eyepiece lenses.
  • Basic principles of virtual images in optical systems.
NEXT STEPS
  • Review the lens formula and its application in microscope calculations.
  • Study the concept of virtual images and their significance in optical systems.
  • Explore the relationship between tube length and magnification in microscopes.
  • Investigate common errors in calculating sample distances in microscopy.
USEFUL FOR

Students studying optics, particularly those working with microscopes, educators teaching optical principles, and anyone involved in laboratory microscopy techniques.

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Homework Statement


A microscope with a tube length of 200 mm achieves a total magnification of 800\times with a 40 \times objective and a 20\times eyepiece. The microscope is focused for viewing with a relaxed eye.
How far is the sample from the objective lens?


Homework Equations


1/s+1/s'=1/f


The Attempt at a Solution


I calculated the two focal lengths for the lenses to be 1/40=0.025m (objective) and 1/20=0.05 m (eyepiece).
Next I calculated the position of the virtual image projected by objective lens. Assuming the final image should be at -25cm the virtual image would be at 4.16cm before the objective lense.
Since there is 20cm between the two lenses this means that the image projected by the objective lens would be at 15.84cm behind the objective lens. Finally I calculated that the object should be at 2.97 cm before the objective lens. However Mastering Physics is telling me this answer is not correct.
Can anyone help steer me in the right direction? Thanks
 
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Magnification Mo = L/fo
Magnification of eye-piece = Me = 25 cm/fe.
 
that would make the focal distances 0.5cm and 1.25 cm for the objective and eyepiece lenses respectively? Using those foci I still do not get the correct answer (0.51 cm).
 

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