Name the type of lens required to obtain 3tymes magnified img of a candle flame on a wall. The candle flame is 6m away from the wall calculate the focal length..???

To obtain a magnified image of a candle flame on a wall, we need to use a converging lens, also known as a convex lens.

To calculate the focal length, we can use the lens formula:

1/f = 1/v - 1/u

Where:
- f is the focal length
- v is the image distance
- u is the object distance

In this case, the object distance (u) is 6 meters since the candle flame is 6 meters away from the wall. The magnification (M) is given as 3 times, meaning the image distance (v) is three times the object distance (u), so v = 3u.

Now, let's substitute the values into the lens formula:

1/f = 1/(3u) - 1/u

Simplifying this equation gives us:

1/f = (1 - 1/3) / u
1/f = 2/3u

To isolate f, we can take the reciprocal of both sides:

f = 3u/2

Substituting the object distance (u) as 6 meters:

f = 3 * 6 / 2
f = 18 / 2
f = 9

Therefore, the focal length required is 9 meters.