Derive expression for the lens maker’s formula i.e.: `frac(1)(f)= (mu-1) (frac(1)(R_1)-frac(1)(R_2))` where the letters have their usual meanings

Prove the following formula when refraction takes place at a convex spherical refracting surface and source of light lies in the rarer medium and image formed is real frac(mu_2)(v)-frac(mu_1)(u)=frac(mu_2-mu_1)(R) Where the terms have their usual meanings.

Show that I = (mu_r-1) H , where the symbols have their usual meanings.

Derive lens formula [frac(1)(v)-frac(1)(u)=frac(1)(f)] for a thin convex lens, using diagram for the formation of a real image by convex Lens.

In the equation : S_(nth)=u+(a)/(2)(2n-1) , the letters have their usual meanings. The dimensional formula of S_(nth) is

Derive Lens formula for [frac(1)(v)-frac(1)(u)= frac(1)(f)] a thin convex Lens, using ray diagram for the formation of a real image by Convex Lens.

In triangle ABC the value of (cot frac (A)(2) cot frac (B)(2)-1) /(cot frac (A)(2) cot frac (B)(2)) is :

Derive the relation:- frac(mu_2)(v) - frac(mu_1)(u) = frac(mu_2 - mu_1) (R) when light undergoes refraction fromoptically rarer to optically denser medium at curved surface.

Starting new cartesian sign conventions, derive the relation. -frac(mu_1)(u) + frac(mu_2)(v) = frac(mu_2-mu_1)(R) , when refraction occurs from rarer to denser medium at convex spherical refracting surface (mu_1 lt mu_2) . Where u, v and R are object distance, image distance and radius of curvature of spherical surface respectively.