I am no expert in the optical branch of physics, but I am very confident that I am correct in stating that a very common myth among amateur/novice photographers is just that - a myth.

The myth I am talking about is something I regularly hear when on wedding assignments or functions. You get this one bloke who knows it all (the speaker), and the impressed audience. The bloke tells his admirers that the reason an SLR is so much better than a compact (non-SLR) camera, is because of the lenses. That you cannot compare say a Canon 70-200mm F2.8L lens with anything on a compact camera.

The myth I believe is that this is simply not true. There is no optical law (or practical constraints) AFAIK that governs big lenses to be better optically than small lenses. In general they tend to be simply due to the nature of economics - professional people tend to buy (expensive) SLR's (which usually happen to be 35mm or larger format), whereas your average snap shooter typically settle for the (less expensive, more manageable) compact cameras. Obviously professional photographers need the best quality so most R&D goes into the design of great SLR lenses. Candid snap shooters are not as fussed about picture quality than pro's - therefore less consideration is paid to the lenses used in those cameras. So I do believe a small lens can be made to the same quality standards than a larger lens.

Furthermore, the size of the lens is only determined by one factor - the imaging circle the lens has to produce on the sensor (film plane). For SLR camera's this is typically 35mm, for compact cameras it can get very small - such as the tiny sensors used in cellphone cameras. Since the f-stop determines the amount of light reaching the film plane, and the f-stop is a relationship between aperture (diameter) and focal lenght, it is therefore obvious that for smaller focal lengths a smaller aperture is required to yield the same f-stop number, i.e. have the same amount of light reach the plane. Therefore the amount of light (i.e. lowest amount of ambient that can be captured without supplimental lighting) is not dependent on the size of the sensor. Smaller sensors require smaller focal lengths for the same angle of view than larger sensors with longer focal lengths.

The reason SLR cameras tend to be better than compact digitals is due to lots of other reasons - but one in specific (applicable to digital cameras, and related to large lenses) is that of the sensor. With the current technology (and any other technology as long as the same level of technological advance is compared), a given sensor will yield lower noise, better dynamic range and just plain better quality pixels the larger it is (within bounds obviously). The fact that dSLR's usually have 1/1.6, 1/1.3 or 1 times the size of a standard 35mm film plane, means they are large and therefore yield much better images than the tiny ones found in most compact digital cameras. See below for a representative comparison:

The reason for this is pure physics regarding the microcell receptors.

Lastly I want to touch on the term MTF (Modulation Transfer Function). This is a measure of how much an image is degraded when passing through any optical lens (actually this is a very high level generalization). For a perfect lens the MTF would be a constant for all lp/mm (a MTF curve is typically plotted for MTF % against lp/mm). In practise, the higher lp/mm spatial frequency one needs from a lens the lower the MTF becomes - and the lower the MTF becomes the less the brightness, contrast and dynamic range becomes. What does this have to do with anything, you might ask? Well, it directly influences the myth. For a given aperture - say f/8, and two cameras - one an SLR and the other a small compact Coolpix 995, the SLR will require a lower lp/mm value to resolve say 4MP of detail than the Coolpix. The reason is obvious - for a given sensor capacity (say 4MP), the pixels is smaller in the smaller sensor and thus more lp/mm (line pair per millimenter) are needed than the bigger sensor. In other words, if a square of 1 mm per side is divided into an area of 16 elements, each element will be 1/4mm = 0.25 mm wide. If a square of 10mm per side is divided into an area of 16 elements, each element will be 10/4mm = 2.5mm wide. Taking the inverse means the 1mm block is divided into 4 l/mm, and the 10mm block is divided into 0.4 l/mm. Thus the larger the block (sensor) the less lines per millimeter are required for the same capacity than a smaller block.

The impact this has is that since a compact camera with a smaller sensor than an SLR will require more lp/mm for a given sensor capacity (say 4MP), the MTF will be much lower than for the SLR. This means for the same MP camera, assuming same lens quality, a compact camera will produce inferior images than a SLR when comparing MTF influence. This is not a lens fault - it is directly related to the sensor size - the fact that a smaller sensor makes a lens work much harder and in less optimal regions than a larger sensor.

So yes - it is more difficult to make a small lens for a compact camera meet the performance of a large lens for a SLR simply because it is more difficult to produce the same MTF for the small compact camera when operating in comparible conditions. But the prime factor is sensor size - NOT lens quality.

Diffraction limit is the limit at which a diffractor (such as a lens aperture) can focus a beam of light. For all practical purposes, this imposes an upper theoretical limit on the resolving power of a lens. Some typical values for red light are:

To put this into perspective, at f/64 (independent of lens), the maximum limit of details is 16 line pairs per millimeter. If a lens is set to a viewing angle of say 45 degrees and focussed at a distance of 10m, it means the arc length projected on the sensor is about 12.7m. If a compact camera's sensor is say 5mm across, it means 12.7m of information is packed in 5mm, and at a resolving power of 16lp/mm it translates roughly to being able to resolve detail larger than 15cm only. So if a person were to stand at 10m distance, chances are you will not recognise him (her). This is one of the reasons small compact cameras are limited to a certain minimum aperture setting - usually f/8. If the sensor was large - like a full frame camera at 35mm, then the same picture would translate to 2.2cm of resolution power - almost better by a factor of 10. That is why SLR cameras can be stopped down much more than smaller cameras.

Once again - it is not the lens at fault here. A lens 1mm in length can perform just as well as a lens of 10m when it comes to diffraction limits, since the diffraction limit is directly proportional to the wavelength of light and to the f-stop - NOT the aperture. It is the sensor size that places the limits on small cameras.