Stargazing Increasing the resolving power of a telescope

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Increasing the resolving power of a toy telescope with a 30mm objective aperture is unlikely to be effective by simply adding a larger convex lens in front. While a larger lens could theoretically gather more light, it may introduce increased aberrations that degrade image quality. A better approach is to focus on increasing the numerical aperture or decreasing the f-number for improved performance. Ultimately, investing in a higher quality telescope is recommended over attempting to modify a low-quality instrument. Upgrading will provide a more significant enhancement in viewing experience.
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I have a toy telescope, very poor objective aperture like 30mm, the image is very poor.

I was wondering if I could increase it's resolving power by placing a convex lens with a larger aperture in front of the objective lens?

The larger lens should converge more light rays onto the objective giving more light.

I understand that the telescope is made for parallel rays but won't decreasing the distance to the eye piece compensate?
 
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You are thinking mostly correctly, but the increased aberrations from doing what you suggest would likely degrade the image further.

What you really need is an increased numerical aperture (decreased f-number), and you are probably better off just getting a better telescope, rather than spending that time and money improving a poor quality instrument.
 
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