Physics Study Guide/Optics

Light

Light is that range of electromagnetic energy that is visible to the human eye, the visible colors. The optical radiation includes not only the visible range, but a broader range of invisible electromagnetic radiation that could be influenced in its radiation behavior in a similar way as the visible radiation, but needs often other transmitters or receivers for this radiation. Dependent on the kind of experimental question light - optical radiation behaves as a wave or a particle named lightwave or photon. The birth or death of photons needs electrons - electromagnetic charges, that change their energy.

The speed of light is fastest in the vacuum.

$c=299,792,458{\frac {m}{s}}$

In a wave we have to distinguish between the speed of transport of energy or the speed of the transport of on phase state of a wave of a defined frequency. In vacuum the speed of waves of any photon energy - wavelength is the same, but the transmission speed through material is dependent on wavelength - photon energy. At the time the measurement of the speed of light in vacuum reached the uncertainty of the unit of length, the meter, this basic unit got in 1960 a new definition, based on the unit of time. Taking the best known measurement values it was defined without any uncertainties of length, that the speed of light is 299,792,458 meters per second. For this reason the only uncertainty in the speed of light is the uncertainty of the realization of the unit of time, the second. (If you like to get the standard of length, cooperate with the watchmaker).

However, when electromagnetic radiation enters a medium with refractive index, $n$ , its speed would become

$c_{n}={\frac {c}{n}}$

where $c_{n}$ is the speed of light in the medium.

Refraction

Refraction occurs when light travels from one medium into another (i.e. from air into water). Refraction is the changing of direction of light due to the changing speed of light. Refraction occurs toward the normal when light travels from a medium into a denser medium. Example when light travels from air into a block of glass, light is refracted towards the normal. The ratio between the sine of the angle of the incident ray and sine of the angle of the refracted ray is the same as the ratios of the indexes of refraction.

${\frac {\sin(\theta _{i})}{\sin(\theta _{r})}}={\frac {n_{r}}{n_{i}}}\quad {\text{or}}\quad n_{i}\sin(\theta _{i})=n_{r}\sin(\theta _{r})$

This is known as Snell's Law - an easy way to remember this is that 'Snell' is 'lens' backwards.

Mirrors and lenses

Focal length

${\frac {1}{d_{i}}}+{\frac {1}{d_{o}}}={\frac {1}{f}}$

• $f$ is the focal length.
  • $f$ is negative in convex mirror and concave lens.
  • $f$ is positive in concave mirror and convex lens.
• $d_{i}$ is the distance from the image to the mirror or lens
  • For a mirror, it is positive if the image appears in front of the mirror. It is negative if the image appears behind.
  • For a lens, it is positive if the image appears on the opposite side of the lens as the light source. It is negative if the image appears on the same side of the lens as the light source.
• $d_{o}$ is the distance from the object to the mirror or the lens (always positive). The only case, when it is negative, is the case, when you don't have a real object, but you do have an imaginary object - a converging set of rays from another optical system.
• an easy way to remember the formula is to memorize "if I Do I Die", which stands for $1/f=1/d_{0}+1/d_{i}$

Magnification

$M={\frac {h_{i}}{h_{o}}}=-{\frac {d_{i}}{d_{o}}}$

• $M$ is the magnification.
  • If it is positive the image is upright
  • If it is negative the image is inverted
• $h_{i}$ is the image height.
• $h_{o}$ is the object height.
• $d_{i}$ is the distance from the image to the mirror or lens (also often $v$)
  • For a mirror, it is positive if the image appears in front of the mirror. It is negative if the image appears behind.
  • For a lens, it is positive if the image appears on the opposite side of the lens as the light source. It is negative if the image appears on the same side of the lens as the light source.
• $d_{o}$ is the distance from the object to the mirror or lens (also often $u$)