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4.1.2.       Refraction of Light & Lenses   <CJ chap 26  >

4.1.2.1. Discussion

4.1.2.1.1.     The Index of Refraction is ratio of the speed of light in vacuum to the speed in the substance

4.1.2.1.1.1. Examples are diamond 2.419, Crown glass 1.523, Benzene 1.501, Water 1.333, Air 1.000293

4.1.2.1.1.2. Refraction of different substances gives prism effect to lead crystal etc

4.1.2.1.2.     Total internal reflection – view from beneath water – how a fish sees the fisherman

4.1.2.1.3.     Total internal reflection used in fiber optics and prisms for binoculars (glass has index of ref = 42 deg)

4.1.2.1.4.     Brewster’s angle: the angle for a substance that polarizes the reflected light with q_reflect=q_refract 

4.1.2.1.5.     Dispersion of light:

4.1.2.1.5.1. Prisms – note red is least diverted (and on the pointed side of prism)

4.1.2.1.5.2. Rainbows: sunlight enters and is internally reflected in water drops: red is bent least (rainbow top)

4.1.2.1.6.     Farsightedness (hyperopic) (use diverging lens) and nearsightedness (myopic) (use converging lens

4.1.2.1.7.     Lenses in combination (see diagrams)

4.1.2.1.8.     Lens aberrations: spherical  and chromatic aberration

4.1.2.2. Mathematical

4.1.2.2.1.     Refraction:

4.1.2.2.1.1. Index of refraction n = c/v where v is the speed of light in the substance (always n >= 1)

4.1.2.2.1.2. Snell’s law of refraction n₁ sin q₁ = n₂ sin q₂ (light passing from media 1 to 2 angles rel. to normal)

4.1.2.2.2.     Total internal reflection

4.1.2.2.2.1. Use Snell’s law with q₂ = 90 deg. To get q_c = sin^-1(n₂ /n₁)

4.1.2.2.3.     Brewster’s Law: q_reflect=q_refract  occurs when tan q_B = n₂ /n₁ and the reflected light is polarized

4.1.2.2.4.     Lenses

4.1.2.2.4.1. Converging lens formula 1/d_o + 1/d_i = 1/f  with magnification  m = h_i /h_o  = - d_i /d_o

4.1.2.2.4.2. Sign conventions:  

4.1.2.2.4.2.1.     f is + for converging lens,  - for diverging lense

4.1.2.2.4.2.2.     d_o is + if object is to the left of the lens (real object) and – if to the right (virtual object)

4.1.2.2.4.2.3.     d_i is + for a (real) image formed to the right of the lens by real object, and –  to the left

4.1.2.2.4.2.4.     m is + for an image that is upright with respect to the object, and – for inverted

4.1.2.2.4.3. Magnifying glass  magnification  m approx.= (1/f – 1/d_i) N where N = dist. of near point to eye

4.1.2.2.4.4. Telescope m approx.=-f_o/f_e where   f_o & f_e  are the focal lengths of the objective and eyepiece lens    

4.1.2.2.4.5. Microscope m approx.= -(L-f_e)N/ (f_of_e) where L is the dist. between the lenses & N is near point

4.1.2.3. Advanced