Take off your glasses and use the diopter, perhaps?
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They are noisier because the entrance pupils of their smaller lenses are generally smaller than on the lenses that provide the same angle of view for larger sensor formats. There are physical limitations in making large entrance pupils for smaller focal lengths, as pupils bigger than f/0.5 are impossible even theoretically.
If you read the thread, you'll understand that my objective was to dispel the notion that f/1.8 on APS-C is in effect the same as f/2.8 on full frame. That notion is actually an unhelpful and circuitous way of saying that APS-C sensors are, because of their typically smaller pixels, usually noisier than full-frame sensors - simple as that.
Given that we have the same angle of view, the amount of light falling on the sensor is purely a function of the pupil diameter. f/2 on full frame is not the same as f/2 on crop.
In case you're still not convinced, now assume that you have a FF and APSC sensor using the same production process & the same overall resolution -- they will have the same sensitivity per photon. If you take a shot with the same shutter speed, given that more light falls on the full frame sensor you would expect to use less sensor signal amplification [ie a lower ISO setting].
The reason why using an f1.8 lens wide open on crop gives a brighter image than f2.8 on FF (when both are at the same ISO and shutter speed) is the amplification of the crop cameras sensor is 2.56x greater, at the expense of noise at any given ISO rating.
What? That's wrong.
A crop f/1.8 lens and a full frame f/1.8 lens will provide exactly the same exposure when used at the same shutter speed and ISO. The full frame exposure WILL NOT be brighter.
You're right about an FF f/2.8 lens having more light gathering ability than a crop f/1.8 lens, but all that light it gathers is spread over a larger sensor, which makes the exposure more than a full stop darker than if you had used an f/1.8 lens.
So in terms of exposure, a f/1.8 lens is brighter than an f/2.8 lens, regardless of sensor size. Sensor size does affect depth of field, but that's a different story.
This is great for crop shooters. However, before everyone gets excited over the f/1.8 bit, you have to remember that f/1.8 on a crop sensor is nothing like f/1.8 on a FF sensor. This lens will give the same angle of view, image noise for given exposure parameters (*1), depth of field at a given AOV and subject distance (*2), etc. etc. etc. as a 28-50mm f/2.8 full frame lens.
In other words, if the lenses and sensors are perfect, this lens on a crop sensor would give identical results to a 28-50mm f/2.8 on a FF sensor.