Light reflection and refraction

• Spherical mirror: \( f=\frac{1}{2}R \)     Concave: \( R>0 \) ; convex: \( R<0 \)

• Mirror equation:   \( \frac{1}{f}=\frac{1}{d_o} + \frac{1}{d_i} \)

• Magnification:   \( m \equiv h_i/h_o = -d_i/d_o \)

Snell's Law

• general:   \( \frac{ \sin{\theta_1} }{ v_1 } = \frac{ \sin{\theta_2} }{ v_2 } \)       EM waves:   \( n \equiv c/v \)   so:   \( n_1 \sin{\theta_1} = n_2 \sin{\theta_2} \)

Total Internal Reflection : (ray moving from higher n to lower n)   \( \sin{\theta_c} = n_{lower} / n_{higher} \)

Lenses and Optical Instruments

• Lens Equation:   \( \frac{1}{ d_o } + \frac{1}{ d_i } = \frac{1}{f} \)         Variants:   \( f = \frac{ d_o d_i }{ d_o + d_i } \)       \( d_o = \frac{ d_i f }{ d_i - f } \)       \( d_i = \frac{ d_o f }{ d_o - f } \)

Magnification:   \( m \equiv h_i / h_o = - d_i / d_o \)

Lens power (diopters):   \( P = 1/f \)   (with f measured in meters)

Lensmaker's equation : lens material n     surrounding material n_o

•   \( \frac{1}{f} = \frac{ n - n_o }{ n_o } ( \frac{1}{R_1} + \frac{1}{R_2} ) \)           in air   n_o=1.000   so     \( \frac{1}{f} = ( n - 1 ) ( \frac{1}{R_1} + \frac{1}{R_2} ) \)

Angular size:   \( \theta \approx (size)/(distance) \)   (from \( s=r\theta \), with \( \theta \) in radians)

Apparent, or angular magnification:   \( M = \theta_{image} / \theta_{object} \)

Random bits

  \( v = \lambda / T = \lambda f = \omega / k \)

  \( k = 2 \pi / \lambda \)     \( \omega = 2 \pi / T \)