1.09 Ray tracing and step along calculations

How to calculate vergence

Vergence (D) = Refractive index / distance from focal point (metres)

Diverging rays have positive/negative vergence

Negative

Converging rays have positive/negative vergence

Positive

Ray tracing through a lens

1. Calculate incident vergence

   1 / distance to surface

2. Calculate vergence after the interface

   V after interface = Vergence + surface power

3. Calculate distance between surface and focal point

   Distance = refractive index / vergence after interface

4. To calculate vergence at any point

   Vergence = Refractive index / distance

Ray tracing a thick lens - calculating the back vertex focal length

1. Calculate incident vergence at F1

   Vergence = refractive index / distance (if infinity then vergence is 0)

2. Determine the effect of lens surface F1 on the vergence of light

   Vergence leaving F1 = incident vergence + power of lens

   Positive vergence - rays will converge

   Negative vergence - rays will diverge

3. Determine the effect of lens thickness on vergence of light

   Back focal length = Refractive index / vergence of F1

4. Calculate vergence at F2

   Vergence at F2 = back focal length of F1 - lens thickness

5. Calculate incident vergence at F2

   Incident vergence at F2 = refractive index / vergence at F2

6. Calculate vergence of rays leaving F2 (back vertex power)

   Vergence of rays leaving F2 = incident vergence of F2 + power of F2

7. Back vertex focal length of F2 (where light will form a focus)

   Back vertex focal length = Refractive index / vergence of rays leaving F2

Back vertex power formula