Lecture 36 Fermats Principle Reflection and refraction Fermats

Lecture 36 Fermat’s Principle Reflection and refraction • Fermat’s Principle • Spherical mirrors • Thin lenses • Magnification

Light as wave and particles • Light is a wave, as discovered by Young et al • It has interference • It has diffraction • We will discuss these properties in late part • However, we also know that light travels on a straight-line, just like particles. • According to Newton, light is a beam of particles • Particle-wave duality: light is particle and but also wave 2

Reflection and refraction 3

Laws of reflection and refraction • 4

Propagation of Light, Fermat’s Principle (1657) • 5

Fermat's principle leads to Snell's law To find the path of least time, set dt/dx=0. Since ni = c/vi and nt = c/vt. Snell’s Law of Refraction

Constructing the image from a plane mirror • Following the light rays to form an image of an object.

The focal point and focal length of a spherical mirror • The focal point is at half of the mirror’s radius of curvature. • All incoming rays will converge at the focal point.

Thin mirrors • A O B 9

Convex spherical mirror

A system of rays may be constructed to reveal the image • Rays are drawn with regard to the object, the optical axis, the focal point, and the center of curvature to locate the image.

Refraction within a sphere • 12

Thin lenses

Thin lenses

Converging lenses •

Magnifying glass • optical axis F

Diverging lens 17

The camera • A clever arrangement of optics with a method to record the inverted image on its focal plane (sometimes film, sometimes an electronic array, it depends on your camera).