Geometrical Optics: How Rays Describe Light
Big idea: geometrical optics models light as straight rays. The model predicts shadows, reflection from mirrors and bending at a boundary between transparent materials.
Learning goals
- distinguish luminous and illuminated objects;
- apply straight-line propagation and the law of reflection;
- describe refraction using refractive index;
- construct the image formed by a plane mirror.
Light sources, rays and shadows
A source emits light; an illuminated object only redirects light that reaches it. In a uniform transparent medium, rays travel in straight lines. An opaque object blocks some rays, producing an umbra. A large source can also produce a partial-shadow region called the penumbra.
Ray diagrams are models: the drawn line shows direction, not a material thread moving through space.
Reflection
At a smooth surface, the incident ray, reflected ray and normal lie in one plane. Angles are measured from the normal, and the law is $\theta_i=\theta_r$. A plane mirror forms a virtual, upright image of equal size at the same perpendicular distance behind the mirror as the object is in front.
Refraction
Light changes speed at a boundary, so its direction may change. The refractive index is $n=c/v$. Snell's law is $n_1\sin\theta_1=n_2\sin\theta_2$. Entering a material with larger $n$, a ray bends toward the normal; entering smaller $n$, it bends away. A ray along the normal does not change direction.