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.

By stating the sign conventions and assumptions used, derive the relation between distance of object, distance of image and radius of curvature of convex spherical surfaces, when refraction takes from optically rarer to optically denser medium.

Obtain lens makers formula using the expression (mu_1)/u + (mu_2)/v = (mu_2-mu_1)/R Here the ray of light propagating from a rare r medium of rerfracitve index (mu_1) to a dneser medium of refractive indes (mu_2) is incident on the convex side of spherical refracting surface of radius of curvature R.

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.

Derive the following relation : log frac (k_2)(k_1) = E_a/(2.303R) [(T_2-T_1)/(T_2T_1)]

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.

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.