PHYS 208 Lecture 24

« previous | Tuesday, November 29, 2011 | next »

Cumulative final exam Fri, Dec 9, at 7:30am.

Light Rays

Straight lines emanating radially outward from a point source.

Wave fronts are always perpendicular to light rays and represent "corresponding points" on an EM wave.

Index of refraction: relation of the electric and magnetic constants for a particular material.

Reflection

Incident angle is taken in respect to the normal of the surface.

Angle of incoming ray and outgoing ray are identical

Refraction

At the boundary of two media, some light can be reflected, but some can continue into the new material

Snell's Law of refraction:

$n_{1}\sin {\theta _{1}}=n_{2}\sin {\theta _{2}}\,\!$

Where $n_{1}$ and $n_{2}$ represent the index of refraction of each medium, and $\theta _{1}$ and $\theta _{2}$ represent the incident angle and the refracted angle, respectively.

Index of Refraction

$n={\frac {c}{v}}$, where $v$ is the speed of light in the medium.

Total Internal Reflection

When exiting a medium with a high relative $n$, there is a point at which the refracted angle is 90°. This is called the critical angle at which all light will be reflected back into the medium. This is how fiber optic cables work.

$n_{1}\sin {\theta _{crit}}=n_{2}\sin {90^{\circ }}$

$\sin {\theta _{crit}}={\frac {n_{2}}{n_{1}}}$

Chapter 34: Geometric Optics

Calculating an Image: Draw two rays from the top of the object at different angles. Trace the rays along the reflection of the mirror. The point where they intersect is the "top" of the image (may be upside-down).

Spherical (and parabolic) mirrors have a focal point at which all parallel incoming light rays meet. For convex mirrors, focal point is where all reflected rays appear to originate.

${\mbox{Magnification}}={\frac {h'}{h}}={\frac {-s'}{s}}$

Where $s$ represents distance, and $h$ represents height. Normal variables are the object's characteristics, and "primes" are the image's characteristics

Mirror Equation

${\frac {1}{s}}+{\frac {1}{s'}}={\frac {1}{f}}$

Where $s$ represents distance and $f$ represents focal distance (positive if in front of mirror, concave; negative if behind mirror, convex).

for spherical mirror, focal point is $f={\frac {R}{2}}$

Thin Lenses

lenses use refraction law to bend light

For the intersection of two surfaces:

• double-convex (intersection of two spheres as in a venn diagram)
• planoconvex (sphere chopped off at plane)
• convex meniscus (sphere cut off at another spherical surface as in a contact lens)

Focal distance is from surface of mirror to focal point (where stuff catches on fire!)