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Qmechanic
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Larger aperture for objective lens in a compound microscope

A telescope has a large aperture to collect more light and hence improve the visibility (brightness) of the image. It also helps in improving the resolution as $\theta_{\text{min}}=\frac{1.22\lambda}{a}$ where $a$ is the radius of the aperture (assuming it to be circular). This led me to wonder why microscopes have small aperture. Yes, under laboratory conditions, the lighting is good; hence a large aperture is not needed to improve the brightness of the image, but from the perspective of resolution of microscope $d_{\text{min}}=\frac{1.22\lambda}{2\tan\beta}$, why don't we design a larger aperture? Is it just for the sake of compactness or is there any theory behind?

Amsterdam6483
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