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

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SUMMARY

The discussion centers on calculating the angle subtended by an image when using a 270-diopter objective lens compared to a 140-diopter lens. The anatomist initially observes an angle of 3.7 x 10-3 radians with the 140-diopter lens. By applying the magnification ratio of the objectives, the angle subtended with the 270-diopter lens is determined to be approximately 0.0019185 radians. The small angle approximation is valid, confirming that the image magnification directly correlates with the objective's refracting power.

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This discussion is beneficial for students in anatomy, biology, and physics, particularly those studying microscopy and optical systems. It is also useful for educators and professionals involved in microscopy and imaging techniques.

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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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