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 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

For a spherical surface,when refraction takes place from a rarer medium (mu_1) to a denser medium (mu_2) , we write -(mu_1)/u + (mu_2)/v = ( mu_2-mu_1)/R where the symbols have their usual meanings. Now suppose that the object is placed in the denser to the rarer medium . Then, rewrite the above equation.