Derive an expression for refraction at a single (convex) spherical surface, i.e., a relation between u, v, R, `n_(1)` (rarer medium) and `n_(2)` (denser medium), where the terms have their usual meaning.

Obtain an expression for refraction at a single convex spherical surface separating the two media having refractive indices mu_(1) (rarer medium) and mu_(2) (denser medium) i.e., a relation between u, v, mu_(1),mu_(2) and R.

Derive R = 2f for a spherical mirror, where the symbols have their usual meaning

Derive the equations s=ut+1/2at^(2) using graphical method where the terms have their usual meaning .

Show that ""^(n)P_r =""^(n-1) P_r + r, ^(n-1) P_(r-1) Where the symbols have their usual meanings.

For any prism, prove that .n. or mu= (sin ((A + delta_(m))/(2)))/(sin ((A)/(2))) where the terms have their usual meaning

Starting with the law of radioactive disintegration, show that : N=N_(0)e^(-lamdat) , where the terms have their usual meaning.

For radioactive disintegration of a radioactive substance, show that N = N_(0)e^(-lambdat) where the terms have their usual meaning,

From energy conservation principle prove the relations, A_r = ((v_2-v_1)/(v_1 +v_2))A_i and A_t = ((2v_2)/(v_1 +v_2))A_i Here, symbols have their usual meanings.