13. (a) Prove that v ^ 2 = u ^ 2 + 2as graphically, where symbols have their usual meanings.

(b) A ship leaves the island of Guam and sails 285 km at 40 deg north of west. In which direction must it now head and how far must it sail so that its resultant displacement will be 115 km directly east of Guam?

14. (a) Show with a ray diagram when convex mirror can form real image.

(b) Derive the mirror formula by using a point object for a concave mirror.

(c) Refractive index is expressed as, u = 1/(sin t) Give the condition for validity of this formula.

(d)What is the maximum and minimum lateral shift produced by a glass slab of thickness 7 cm? Draw ray diagrams for them.

(e) Obtain the formula, u = (Real depth)/(Apparent depth)

solve all these questions with proper explanation