**I want to find the nearest 50(or 80, even 100)solutions under 1.4628 from big to small**, I tried FindInstance function in MMA, but still cannot get the desired results I need.Here is my code:

`Clear["Global'*"]; $ RecursionLimit = Infinity; nco = 1.4681; ncl = 1.4628; nair = 1; rco = 4.2*10^3; rcl = 62.5*10^3; \[CapitalDelta]n = ncl - nair; wl = 1000; u = 2*\[Pi]*rcl*((ncl^2 - neffcl^2)^((1/2))/wl); w = 2*\[Pi]*rcl*((neffcl^2 - nair^2)^((1/2))/wl); J0 = BesselJ[0, u]; J1 = BesselJ[1, u]; K0 = BesselK[0, w]; K1 = BesselK[1, w]; N[ FindInstance[ J1/(u*J0) == (1 - 2*\[CapitalDelta]n)*(K1/(w*K0)) && 1.45 < neffcl < 1.463, neffcl, PositiveReals, 50] ] TM Plot[{J1/(u*J0), (1 - 2*\[CapitalDelta]n)*(K1/(w*K0))}, {neffcl, -2, 2}] Plot[{J1/(u*J0), (1 - 2*\[CapitalDelta]n)*(K1/(w*K0))}, {neffcl, 1.453, 1.463}, PlotRange -> {-0.005, 0.005}] `

I plotted two pictures, the first one represent the solutions of the unsolved function, and in the 2nd one, I plotted the formula with neffcl from 1.453 to 1.463.

As for the given results, we can see that MMA only returns 15 solutions, not 50 I set, but we can see both in the first and 2nd picture that there is absolutely more than 15 solutions for my formula, here is what MMA returns:

`{{neffcl -> 1.45092}, {neffcl -> 1.45193}, {neffcl -> 1.45289}, {neffcl -> 1.4538}, {neffcl -> 1.45467}, {neffcl -> 1.45549}, {neffcl -> 1.45628}, {neffcl -> 1.45701}, {neffcl -> 1.45835}, {neffcl -> 1.45951}, {neffcl -> 1.4622}, {neffcl -> 1.46241}, {neffcl -> 1.46257}, {neffcl -> 1.46269}, {neffcl -> 1.46277}} `

picture1 Picture2

Somebody can tell me what is wrong with my code and how can I make it work? Thanks in advanceļ¼