$5\mathrm{.}14\mathrm{.}1.($a$)$If c $$is a function only of z$,$show that dds$=-[$cos$0$c$0]$dcdz$,$with $0$the

angle of elevation of the ray where c$=$c$0.($b$)$If the gradient g$=$dcdz $$is a constant,

find the radius of curvature R $$of the ray in terms of g$,$c$,$and $.$Is R $$a constant?

$($c$)$If the temperature of air decreases linearly with height z$,$verify that c$($z$)=$c$0-$gz$,$

where g$>0.$If the temperature decreases $5$C$$km$,$find the radius of curvature of

a ray that is horizontal at z$=0($assume c$0=340$ms$).$At what horizontal range

will this ray have risen to a height of $10$m$?$