Concept Summary

Electromagnetic Spectrum

• Electromagnetic waves are transverse waves that consist of an oscillating electric field and an oscillating magnetic field.
• The two fields are perpendicular to each other and to the direction of propagation of the wave.
• The electromagnetic spectrum is the range of frequencies and wavelengths found in EM waves.
• The EM spectrum includes, from lowest to highest energy, radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and γ-rays.
• The visible spectrum runs from approximately 400 nm (violet) to 700 nm (red).

Geometrical Optics

• Reflection is the rebounding of incident light waves at the boundary of a medium.
• The law of reflection states that the incident angle will equal the angle of reflection, as measured from the normal.

• Spherical mirrors have centers and radii of curvature, as well as focal points.

  • Concave mirrors are converging systems and can produce real, inverted images or virtual, upright images, depending on the placement of the object relative to the focal point.
  • Convex mirrors are diverging systems and will only produce virtual, upright images.
  • Plane mirrors also produce virtual, upright images; these images are always the same size as the object. They may be thought of as spherical mirrors with infinite radii of curvature.
• Refraction is the bending of light as it passes from one medium to another.
• The speed of light changes depending on index of refraction of the medium. This speed change causes refraction.
• The amount of refraction depends on the wavelength of the light involved; this behavior causes dispersion of light through a prism.
• Snell’s law (the law of refraction) states that there is an inverse relationship between the index of refraction and the sine of the angle of refraction (measured from the normal).

• Total internal reflection occurs when light cannot be refracted out of a medium and is instead reflected back inside the medium.

  • This happens when light moves from a medium with a higher index of refraction to a medium with a lower index of refraction with a high incident angle.
  • The minimum incident angle at which total internal reflection occurs is called the critical angle.

• Lenses refract light to form images of objects.

  • Thin symmetrical lenses have focal points on each side.
  • Convex lenses are converging systems and can produce real, inverted images or virtual, upright images.
  • Concave lenses are diverging systems and will only produce virtual, upright images.
  • Lenses with non negligible thickness require use of the lensmaker’s equation.

• The following table summarizes image creation in converging and diverging systems for both mirrors and lenses:

	Converging Systems					Diverging Systems
o relative to f	o > 2f	o = 2f	2f > o > f	o = f	o < f	all object distances
image	real, inverted, reduced	real, inverted, same	real, inverted, magnified	no image	virtual, upright, magnified	virtual, upright, reduced

Diffraction

• Diffraction is the bending and spreading out of light waves as they pass through a narrow slit.
• Diffraction may produce a large central light fringe surrounded by alternating light and dark fringes with the addition of a lens.
• Interference supports the wave theory of light.
• Young’s double-slit experiment shows the constructive and destructive interference of waves that occur as light passes through parallel slits, resulting in minima (dark fringes) and maxima (bright fringes) of intensity.

Polarization

• In plane-polarized light, all of the light rays have electric fields with parallel orientation.
• Plane-polarized light is created by passing unpolarized light through a polarizer.
• In circularly polarized light, all of the light rays have electric fields with equal intensity but constantly rotating direction.
• Circularly polarized light is created by exposing unpolarized light to special pigments or filters.