The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall 3m away by means of a large convex lens. What is the maximum posible focal length of the lens required for the purpose ?

Explanation

`(1)/(v) - (1)/(u) = (1)/(f) - u + v = 3,` here, v = 3 + u
` (1)/(3 + u) - (1)/(u) = (1)/(f) " i.e.," f = - ((u^(2) + 3u)/(3) ) `
For .f. to be maximum , `(df)/(du) ` = 0
ie., `(df)/(du) = - (1)/(3) [ 2u + 3] = 0 therefore u = (-3)/(2) " " therefore v = 3 + u = 3 - (3)/(2) = (3)/(2) `
`therefore (1)/(f) = (1)/((3)/(2)) - (1)/((-3)/(2)) = (2)/(3) + (2)/(3) = (4)/(3) " " therefore f = (3)/(4) = 0.75` m