Refraction Bends Light to Form an Image
Why a straw looks bent where it enters water, how glasses and cameras form an image, and how an optical fiber traps light to carry a signal all come from one fact. Light changes speed when the medium changes, so it bends direction at a boundary. We write this refraction with a single Snell's law, and we predict the position and size of an image with the lens equation 1/f = 1/u + 1/v.
When light passes into a different medium its speed changes, and that is why it bends at the boundary. The bending is governed by Snell's law, n1 sinθ1 = n2 sinθ2. The denser the medium it enters, the more the light hugs the normal. The refractive index n is the speed of light in vacuum divided by its speed in the medium, so it tells you how much the light slows down there. Move the incidence angle and n2 to watch the refracted angle follow.
When light leaves a denser medium for a thinner one, the refracted angle is larger than the incidence angle. Keep raising the incidence angle and there is a moment when the refracted angle reaches 90 degrees; that angle is the critical angle θc = asin(n2/n1). Beyond it, none of the light gets out and all of it reflects. An optical fiber uses exactly this total internal reflection to trap light and carry it far. A diamond has a very high refractive index and thus a small critical angle, so light that enters it bounces by total internal reflection many times and sparkles.
A thin lens forms an image by refraction alone. The object distance u, image distance v, and focal length f obey 1/f = 1/u + 1/v. If the object sits beyond the focal point, an inverted real image appears on the far side; bring it inside the focal point and an upright virtual image appears on the same side. A magnifying glass, which enlarges by keeping the object inside the focal length, is exactly an application of this virtual image. Push and pull the object to see where the image lands and how large it grows.
The sign of the focal length sets the character of the lens. A positive f is a converging lens that gathers light; a negative f is a diverging lens that spreads it. A diverging lens always makes a small, upright, virtual image. The magnification is m = -v/u, whose sign tells you upright versus inverted and whose size tells you enlarged versus reduced. Eyeglasses that correct nearsightedness are diverging lenses with a negative f, spreading the incoming light beforehand so the image lands on the retina. Slide f across zero to watch the image switch between real and virtual.
Where the image forms can be constructed with just three principal rays. A ray arriving parallel to the axis passes through the focus after the lens; a ray through the center of the lens goes straight without bending; and a ray through the near focus emerges parallel to the axis behind the lens. The point where the three rays meet again is the image point. In fact, two rays are enough to locate the image, and the third ray works as a check that the result is right. Drag the object and confirm that the three rays always reconverge at the same spot.