light

• Total internal reflection occurs when light travels from a material with a high index of refraction to a material with a low index of refraction
• Total internal reflection will not occur between water and diamond, but it can occur as light travels from water to air
• Total internal reflection only occurs if the incident angle exceeds the critical angle
• The critical angle is the incident angle when the refracted angle is 90
• To calculate the critical angle, use Snell's Law: n1 sine(theta1) = n2 sine(theta2)
• For air and water, the critical angle is about 48.75 degrees
• If the incident angle exceeds the critical angle, there is no more refraction and only reflection occurs, leading to total internal reflection
• For glass and water, the critical angle is about 62.5 degrees
• To find the index of refraction for a solid given a critical angle of 40 degrees with air, use n1 sine(90) = n2 sine(40)
• The index of refraction for the solid is 1.56
• Principal axis is the horizontal line in concave and convex mirrors
• Concave mirror has the focal point and center on the left side, while the convex mirror has them on the right side
• Focal length is half of the radius of curvature
• Left side of the mirror is usually the front side where the object is placed, right side is the back side or behind the mirror
• Object distance (do) is positive for a real object, negative for a virtual object
• Image distance (di) is positive for a real image, negative for a virtual image
• For concave mirrors, focal length is positive; for convex mirrors, focal length is negative
• Magnification (M) is the ratio of image height to object height, M = -di/do
• If magnification is positive, the image is upright; if negative, the image is inverted
• If |M| > 1, the image is enlarged; if |M| < 1, the image is reduced
• For concave mirrors, if the object is beyond the center of curvature, a real, inverted, and reduced image is formed
• If the object is between the center of curvature and the focus, a real, inverted, and enlarged image is formed
• If the object is at the center of curvature, a real, inverted, and same-sized image is formed
• If the object is between the focus and the mirror, a virtual, upright, and enlarged image is formed
• If the object is at the focus, no image is formed
• For convex mirrors, if the object is in front of the mirror, a virtual, upright, and reduced image is formed
• If the object is behind the mirror, a virtual, upright, and enlarged image is formed
• For a concave mirror:

  • The principal axis is a horizontal line
  • The focal point is the point where the light rays converge
  • The distance between the focal point and the mirror is the focal length
  • The distance between the object and the mirror is d_o
  • The height of the object is h_o
  • The image is located where the rays intersect
• The type of image depends on the location and characteristics:

  • Real image: Light rays converge at the image location
  • Virtual image: Light rays appear to converge at the image location
• Magnification:

  • If the height of the image is greater than the height of the object, magnification is greater than one (enlarged image)
  • Positive magnification: Upright image
  • Negative magnification: Inverted image
• For a concave mirror with the object between the focal point and the mirror:

  • The image is upright
  • The image is enlarged
  • The image is virtual
• For a convex mirror:

  • The image is virtual
  • The image is upright
  • The image is reduced in size
• For a divergent lens:

  • The focal length is negative
  • The image is virtual
  • The image is reduced in size
  • The image is upright
• For a convergent lens:

  • The focal length is positive
  • The image can be real or virtual depending on the object's location
  • Real image: Light rays converge at the image location
  • Virtual image: Light rays appear to converge at the image location
• Concave or diverging lenses cause light rays to diverge and spread out
• Concave lenses get wider towards their ends
• Symbol for concave lens in ray diagrams: outward pointing V shapes at either end
• Axis: horizontal line through the middle of the lens
• Focal points: one on either side, also known as principal focus
• Additional point labeled 2f on either side, twice as far away from the lens as the focal point