reset # clear all styles, variables ...

# SVG output
set terminal svg size 800,400 fname 'Verdana, Helvetica, Arial, sans-serif
set output 'airyformel.svg'

set samples 1001 # enough points to make it look nice

# set font sizes for labels, legend and title
set xtics  font ",16" 
set xlabel font ",16"

set ytics  font ",16"
set ylabel font ",16"

set key   font ",20"
set title font ",20"
set label font ",20"

set grid # activate grid to indicate position of dips and peaks
set xrange[0:2*pi]  # function is pi-periodic
set yrange[0:1]     # it's normalized

# set labels with unicode greek letters
set xlabel 'φ=2π ν/(∆ν)'
set ylabel 'I/I_{max}'

# set grid lines where it's important for the understanding
set xtics ('0' 0,\
     'π/2' pi/2,\
     'π' pi,\
     '3π/2' 3*pi/2,\
     '2π' 2*pi)

set ytics('0' 0,\
     '0.5' 0.5,\
     '1' 1)

# line colors copied from viridis colormap by Eric Firing
# licensed under CC0 https://creativecommons.org/publicdomain/zero/1.0/
# https://github.com/Gnuplotting/gnuplot-palettes/blob/master/viridis.pal
set style line  1 lw 2 lt 1 lc rgb '#440154' # dark purple
set style line  2 lw 3 lt 1 lc rgb '#2c718e' # blue
set style line  3 lw 3 lt 1 lc rgb '#aadc32' # lime green

# modified the formula,  so you just have to insert another value for Finesse ℱ
I500(x) =1/(1+(2*500/pi)**2*(sin(x))**2)
I50(x)  =1/(1+(2* 50/pi)**2*(sin(x))**2)
I5(x)   =1/(1+(2*  5/pi)**2*(sin(x))**2)

set key top right # legend in the upper right

# set arrows to indicate the linewidth 
set style arrow 1 head filled size screen 0.03,15 ls 2 front
set arrow  from pi*4/5, 0.5 to pi*49/50,0.5 as 1
set arrow  from pi*6/5, 0.5 to pi*51/50,0.5 as 1 

set label 'δ∝∆ν/ℱ' at first pi*6/5, 0.502 font ",20"  # label next to arrow

plot I500(x) ls 1 title 'ℱ=500',\
	  I50(x) ls 2 title 'ℱ=  50',\
	   I5(x) ls 3 title 'ℱ=    5'

unset output # close file