Any help much appreciated - this is driving me crazy!(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Show that the focal length of a half ball lens, in air, (in the paraxial limit) is given by:

f=R/n-1

2. Relevant equations

Equation (from Hecht- Optics), for refraction at a spherical interface:

n_{m}/s_{0}+ n_{l}/s_{1}= (n_{l}-n_{m})/R

where,

n_{m = refractive index of medium nl = refractive index of lens material s0 = distance from object to surface s1 = distance from image to surface 3. The attempt at a solution Setting s0 = ∞ Then s1 = f Subbing into the equation gives, nm/s0 + nl/s1 = (nl-nm)/R 0 + nl/f = (nl-nm)/R f = Rnl/nl-1 Where am I going wrong with this? Thanks.}

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Focal Length of a Half Ball Lens

**Physics Forums | Science Articles, Homework Help, Discussion**