Physics: Optics- Thick Lenses (23 of 56) The System Matrix Analyzed

In this video I will explain and analyze the system matrix with a 3-lens compound lens.

Next video in this series can be seen at:

[reyyanuysal]

Sir how can be a_12 the negative of inverse of the effective focal length? Where does this result come from?

[bingsenlim]

Hi sir may I know how you get the last equation at the bottom that relates a_12 to the focal length and refractive index? If possible, can you also show me or provide a link to the derivation of the equation shown in video 8 of the playlist? I asked this because I got contradicting results when I try to use this equation to derive the Len's maker equation for thick lens in a medium (as shown in video 8 of this playlist). Let n_m denote the refractive index of medium and n denote the refractive index of the lens, after expanding the system matrix for a thick lens and factorizing it I got a_12 = - (n-n_m) (1/R_1 - 1/R_2 + (n-n_m)d/nR_1R_2) . If this is equal to -n_m/f as shown in this video, then 1/f = ((n-n_m)/n_m) (1/R_1 - 1/R_2 + (n-n_m)d/nR_1R_2), which is slightly different from the equation you have shown in video 8. In this case, may I know which formula is wrong, or which part of my derivation is wrong? Thank you very much.