The f/stop system of numbering is specially invented to ensure that different lenses at the same f/stop number will see the same exposure. This includes your wide angle and telephoto lenses. F/stop number = focal length / effective aperture diameter.

Also, the wide angle lens can collect more overall total of photons (from a wider area). However a focal length 2x longer (100 mm vs 50 mm) does make the subject appear 2x larger, except our telephoto lens crops our view into 1/4 the area still visible. Assuming our subject was a large evenly lighted blank wall (no special areas to complicate this), then we see 1/4 the light (photons, your argument), but in 1/4 the area, which is the same light per unit of area. Exposure is about light per unit of area, Not about total photons in the whole frame area.

The f/stop system of numbering is specially invented to ensure that different lenses at the same f/stop number will see the same exposure. This includes your wide angle and telephoto lenses. F/stop number = focal length / effective aperture diameter.

Also, the wide angle lens can collect more overall total of photons (from a wider area). However a focal length 2x longer (100 mm vs 50 mm) does make the subject appear 2x larger, except our telephoto lens (and same sensor size) crops our view into 1/4 the area still visible. Assuming our subject was a large evenly lighted blank wall (no special areas to complicate this), then we see 1/4 the light (photons, your argument), but in 1/4 the area, which is the same light per unit of area. Exposure is about light per unit of area, Not about total photons in the whole frame area (a bright right hand edge of frame adds photons, but does not change the proper exposure of a dark left hand side).