What is the focal length of a lens that produces a real image three times as large as theobject if the distance between image and the object is 1 m?

To find the focal length of the lens, we can use the lens formula:

1/f = 1/v - 1/u

Where: f is the focal length of the lens v is the distance between the image and the lens u is the distance between the object and the lens

Given that the distance between the image and the object is 1 m, we can assume that v = 1 m.

Since the image is three times larger than the object, we can say that the magnification (M) is equal to 3. The magnification is given by:

M = -v/u

Rearranging the equation, we can solve for u:

u = -v/M

Substituting the given values, we have:

u = -1/3

Now, we can substitute the values of v and u into the lens formula:

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

Simplifying the equation, we get:

1/f = 1 - (-3)

1/f = 1 + 3

1/f = 4

Therefore, the focal length of the lens is 1/4 or 0.25 meters.