What angle is subtended when using this 270-diopter objective?

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Homework Help Overview

The problem involves an anatomist using a microscope with two objectives of different refracting powers, specifically focusing on how the angle subtended by an image changes with the objective's strength. The subject area relates to optics and the behavior of light through lenses.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the angle subtended by an image and the refracting power of the microscope objectives. There is an exploration of the small angle approximation and its implications for solving the problem.

Discussion Status

Some participants have offered insights into the expected behavior of the angle with increased objective strength, suggesting a proportional relationship. However, there remains some uncertainty about the application of these concepts, as one participant expresses confusion regarding the approach.

Contextual Notes

There is a mention of the small angle approximation being valid for the angles involved, which may influence how the problem is interpreted and approached. Additionally, the original poster indicates uncertainty about their initial calculations and methodology.

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Homework Statement


An anatomist is viewing heart muscle cells with a microscope that has two selectable objectives with refracting powers of 140 and 270 diopters. When she uses the 140-diopter objective, the image of a cell subtends an angle of 3.7 x 10-3 rad with the eye. What angle is subtended when she uses the 270-diopter objective?


Homework Equations


tan alpha=h/f


The Attempt at a Solution


h=tan(3.7x10^-3)(140) = 0.518
tan beta = 0.518/270
beta = 0.0019185 rad


This is incorrect... I am not sure if I'm even going about this problem the right way. Thanks for any help you can give!
 
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Note the small angle involved (3.7 x 10^-3 rad), so the small angle approximation is valid
θ ≈ sinθ ≈ tanθ​
The image will simply be magnified in proportion to the power of the objective.
 
I don't really understand what this means.. how are you saying I would go about solving this with that in mind?
 
The image originally subtended an angle of 3.7 x 10^-3 rad.

Using a stronger objective, we expect the image to appear larger.

Since the objective strength has been increased by a ratio of (270/140), the 3.7 x 10^-3 rad angle will get multiplied by that same factor.
 
Ohh, I was making it harder than it should be. Thank you very much!
 

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