Small Aperture difference - A big difference?

I had a second a second thought about asking this question because I have already asked a very similar question here but then I decided to proceed and make this one as different as possible.

I understand the fact that the light entering the camera is directly proportional to the square-root of the aperture. The maximum aperture I can get in my Fujifilm Finepix S2980 is f/3.2. Still I'm not getting satisfactory dim-light performance(I don't want to use a flash). Some friends suggested me that I should go for a camera(perhaps something like a DSLR) with a better sensor and f/1.8 or f/1.4 lens.But as I don't want to become a photographer by profession, I need to think twice before I leap because of the high cost factor associated with these cameras and lenses.

The first question I need to address is whether a lens with an aperture f/1.4 or f/1.8 perform considerably better than a f/3.2 lens(let us assume same shutter speeds) in dim light conditions.I haven't dealt neither with f/1.8 nor with f/1.4 lens before. I would like to see your suggestions based on real-life experiences.

Note: Fujifilm Finepix S2980 is a point and shoot camera with 14MP maximum resolution 18x Optical Zoom with some handy Face Detection,Auto-Focus and Image Stabilisation options.

The aperture affects exposure because it is the area of the opening in the diaphragm that lets light through. At f/2.8, the area of the aperture is twice as much than at f/4. We can verify this by calculating the actual diameter and area of the aperture for any given lens. Lets use a 50mm, 100mm and 300mm lens as examples.

The table below shows the diameter of the apertures of each lens at various settings:

Lens  | f/1.4    | f/2     | f/2.8    | f/4
===============================================
50mm  | 35.71mm  | 25mm    | 17.85mm  | 12.5mm
100mm | 71.23mm  | 35.71mm | 25mm     | 17.85mm
300mm | 214.29mm | 150mm   | 107.14mm | 75mm


As you can see from the above table, diameter increases for any given aperture as focal length increases. Diameter doesn't really tell you the exposure story, though. If we compute the area of the aperture for each of these lenses (area = πr^2):

Lens  | f/1.4     | f/2       | f/2.8    | f/4
====================================================
50mm  | 1002mm^2  | 491mm^2   | 250mm^2  | 122.7mm^2
100mm | 4007mm^2  | 1963mm^2  | 1002mm^2 | 491mm^2
300mm | 36064mm^2 | 17671mm^2 | 9016mm^2 | 4417mm^2


I think seeing the differences in terms of area helps demonstrate why a small difference in the aperture number means a big difference in exposure. I think it also demonstrates why long lenses with fast apertures are capable of gathering so much more light than short/wide lenses with fast apertures.

From the areas above, you can see that any of the lenses, 50mm, 100mm, or 300mm, will all gather about four times as much light at f/1.4 than at f/2.8. The same would be true for an f/1.8 lens vs. an f/3.5 lens...a four-fold difference in light. In terms of light gathering ability, a fast f/1.4 or f/1.8 lens will indeed be considerably better than an f/3.5 lens. But thats just talking about exposure.

The wider the aperture, the more likely you are to encounter optical aberrations, which can potentially degrade image quality beyond what an f/3.5 aperture might. You also have to consider depth of field requirements...narrower apertures increase the depth of field, while very wide apertures make it razor thin. How well a lens performs is not solely based on how wide its aperture is. Maximum aperture simply puts a cap on your ability to photograph without lots of noise in dim light.

From 3.2 to 1.8 is a little over 3 times the amount of light - yeah, it makes a difference. If you still want something that is a pocketable camera, but great quality look at the Sony RX100 (review here).

The Fuji you have has a really small sensor, which is going to limit low-light ISO performance. The RX100 has a sensor 4 times larger than your Fuji. Not only is the higher ISO performance of the RX100 far better than your Fuji, the lens is f/1.8 - so you'll be increasing the ability to take low light images in 2 ways.

• +1 for the link. I didn't know there are such fast pocket cameras for such an affordable price. Seems to me like a very sensible alternative for the OP instead of upgrading to a DSLR. Sep 20, 2012 at 19:18

Aperture is measured as a ratio of focal-length to iris diameter and each stop lets twice as much light as the previous one, so yes a small numerical difference can make a big difference.

Here is an example with round numbers: F/2.8 is one stop over F/2 which is one stop over F/1.4. So, F/2 lets twice as much light as F/2.8 and F/1.4 lets twice as much as F/2, so FOUR times as much as F/2.8.

Now you can find bright F/2 or better lenses on a compact camera as well as on DSLRs. DSLRs however have much larger sensors so they use longer lenses. Because aperture is a ratio, an F/2 lens on a DSLR has much bigger aperture than an F/2 lens on a compact camera.