Magnification using telescope or binoculars: We see with an eye brain combination. Early in life, we learn gauge distances comparing object size intertwined with an involuntary perception of the “visual angle” induced by distance.
Example: A friend holds a yard stick, 10 feet distant. You sweep your eyes over the stick, end to end. Your eye sweeps a visual angle of 17°. If your friend withdraws to 20 feet, the visual angle becomes to 8 ½ °.
If we gaze through a telescope, we see a magnified view. The telescope or binoculars sports a converging lens, upfront called the “objective lens”. This lens alters angle of the arriving light rays. Rays, as they pass through the objective lens are caused bend inward (refract). The revised path traces the shape of a cone. An image of the vista is caused to form in air, behind the lens. We can view this image if we interpos a piece of white paper as a projection screen. We see this projection as an upside-down miniature image, in full color, of the vista.
We set another lens, with less power (less focal length), behind projected image. The second lens, called an “eyepiece” magnifies the projected image. When all is focused correctly, the light exits the eyepiece as parallel rays. We gaze at this image. Our eye/brain is fooled. We think we see light rays coming straight as an arrow to our eyes. We cannot sense that the rays have converged and then diverged. The result is; we see an altered visual angle that generates a magnified view.
The amount of magnification is the size we see with our unaided eyes vs. the size we see when looking through this instrument. The magnification amount (power) is the focal length of the objective lens multiplied by the focal length of the eyepiece lens.
We put some finishing touches on this instrument. We add lenses to invert the image to right-side-up. We add prisms to shorten the physical length of the instrument.