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Im thinking if I can obtain parallel rays after the light rays pass through the convex lens by moving the lens closer to the light bulb or by having a lens with a larger focal length. Which method is right?

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As drawn you can move the (point) light source towards the lens to produce a parallel beam of light when the light source is at the foal point of the lens.
This then tells you that you need a lens of larger focal length if you want to produce a parallel beam without changing the lens to light source distance.

I cannot tell you which method is right because they both produce the required parallel beam of light

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