Lens Equation
The relationship between object distance (d₀), image distance (dᵢ), and focal length (f) is given by:
1/f = 1/d₀ + 1/dᵢ
Where:
- f is the focal length of the lens
- d₀ is the distance from the object to the lens
- dᵢ is the distance from the image to the lens
Magnification
The magnification (M) is the ratio of image height to object height:
M = hᵢ/h₀ = -dᵢ/d₀
Where:
- hᵢ is the image height
- h₀ is the object height
- dᵢ is the image distance
- d₀ is the object distance
Principles of Geometric Optics
Geometric optics describes light propagation in terms of rays. The three principal rays used to locate images are:
- Parallel Ray: Parallel to the axis, passes through the focal point after refraction
- Focal Ray: Passes through the focal point, emerges parallel to the axis
- Central Ray: Passes through the center of the lens undeviated
Image Characteristics
Depending on the object position relative to the focal point:
- Real Image: Formed when light rays actually converge
- Virtual Image: Formed when light rays appear to diverge
- Upright or Inverted: Determined by the sign of magnification
- Magnified or Reduced: Determined by the absolute value of magnification