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

[phys62]

1. The problem statement, all variables and given/known data
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?


2. Relevant equations
tan alpha=h/f


3. 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!!

[Redbelly98]

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.

[phys62]

I don't really understand what this means.. how are you saying I would go about solving this with that in mind?

[Redbelly98]

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.

[phys62]

Ohh, I was making it harder than it should be. Thank you very much!