A student has to project a three times magnified image of a candle flame on a wall. Name the type of the lens (converging/diversing) required for the purpose. If the candle flame is at a distance of 6 m from the wall, find the focal length of the lens.

Options

A. converging , `f = 1.125 m`
B. converging , `f = 1.125 cm`
C. diverging, `f = 1.125 m`
D. diverging, `f = 1.125 cm`

Answer

A

Explanation

Here, `m = -3`
As image is formed on the wall, the lens must be converging.
As `m = v/u = 3, v = 3u`, in magnitude.
As candle flame is at a distance of 6 m from the wall,
`:. u + v = 6 or u + 3u = 6, u = 6/4 = 1.5 m`
`v = 3u = 3 xx 1.5 = 4.5 m`
With proper sign convention,
`u = -1.5 m, v = +4.5 m`
`1/f = 1/v - 1/u = 1/(4.5) - 1/(-1.5) = (1+3)/(4.5)`
`f = (4.5)/4 = 1.125 m`