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I know increasing the size of the photo (S,M,L) does not affect the dpi, but refers only to the pixels. My camera shoots at 300 by default, but sometimes I want a crisper look when I get larger prints. I can print a 4x6, then scan it and save at the higher resolution, but that is SO time consuming. Does anyone have a solution to changing the camera setting? It might not even be possible, or maybe I need a newer, updated camera. (I use a Nikon D40x, with a AF-S 70-300mm lens for most pictures.)

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You got it the wrong way round; the dpi setting stored in the file is nowadays just a historic and mostly useless number, and you could simply change it with a tool, but there is not even any need for printing.

What you need to care for is the total resolution of the photo, which is limited by the camera hardware. You can reduce resolution, but never increase it (you can fake it by doubling the number of pixels and interpolating the missing values with noise - which is what you describe by scanning it back in). You should always use the L setting to get the maximum number of pixel the camera can produce

The resolution is defined by the camera hardware - professional grade cameras typically have 20+ Mpixel, some up to 50 MPixel; consumer cameras between 5 Mpixel and 20 Mpixel. If you want a higher resolution, the only way is to buy a better camera.

If you want to print larger, you need more pixel = more resolution. For a 10x15 inch print in good quality, you need 1500 x 2250 pixel (which is about 3 MPixel), that should be easy to achieve with any camera nowadays.

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    \$\begingroup\$ inhowfar, @Rafael? If a file is 1000 pixel, and I ask my printer to print it 5 inch wide, what does it matter if the file was set to 300 or 200 or whatever dpi? I haven't seen a print program or driver for at least 15 years that doesn't ignore the DPI setting in the file and allows you to print it however large you'd like to print it. I can also set my files to 1000000 DPI or 0.0001 DPI and no software takes any notice. Note that I am not saying DPI as a number during the printing process is meaningless (it isn't), I am saying the DPI number stored within a graphics file is meaningless. \$\endgroup\$
    – Aganju
    Commented Jun 23, 2016 at 16:17
  • \$\begingroup\$ @Rafael It's meaningless because dpi stands for dots per inch, but the size of the displayed or printed image in inches isn't determined until the image is actually displayed or printed. Furthermore, depending on how the image is displayed or printed, the full resolution of the image may not even be used. Since neither the number of dots actually displayed nor inches used to display them are known when the file is written, it's hard to see what real meaning the dpi figure can have without making arbitrary and probably incorrect assumptions. \$\endgroup\$
    – Caleb
    Commented Jun 23, 2016 at 16:49
  • \$\begingroup\$ @Rafael I'd agree that it's possible to assign some meaning to the number, or to set the value to match the print/display conditions in which you expect to use the image, but if you already know the display size and pixel dimensions of the image, the dpi value can be calculated. You keep saying that the number is not meaningless, so: what does that dpi value mean to you? \$\endgroup\$
    – Caleb
    Commented Jun 23, 2016 at 17:07
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    \$\begingroup\$ Hey, i just accepted the arguments, and adjusted it... I thought that's what was the point of the arguing... \$\endgroup\$
    – Aganju
    Commented Jun 23, 2016 at 18:00
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    \$\begingroup\$ And, yeah, the comments can now all be cleaned up :) \$\endgroup\$
    – mattdm
    Commented Jun 23, 2016 at 18:05
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I can print a 4x6, then scan it and save at the higher resolution.

Why would you do that! Where is the magic process that creates new detail there? You are only losing information!

You are cheating on yourself, you probably are seeing more contrast, because you are loosing middle tones, you probably are watching the paper texture, but you are NOT getting "crisper look".

This is important because as you are confused about what you see you can not replicate it with the proper steps in post processing. As I say, more contrast, different saturation, some noise, etc.

  1. Use L. Forget about s and m.

  2. Apply sharpen on any program. Yes you could shoot at RAW etc. But sharpen is something that can be applied into any JPG image and makes it... sharper.

About the resolution. With your 10 Megapixels (3872 x 2592 pixels) you can print a 19.3x12.9 inches image. (a good standard is to use 200 ppi) or a 25.8x17.2 with 150 ppi. which is still good resolution.

If your image is not sharp enough you probably have a focus problem, motion blur, dirty lens, or simply your lens is not sharp enough.

You need to review your process. Probably use a tripod, focus on live view, reduce the aperture, etc, to make the image as good as your camera and lens can.

Then go to post processing and improve it.

But please, do not ever again print it and scan it.

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