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?
Question
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?
Solution
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.
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