magnification produced by a convex lens of focal
length f?
A. u + f
B. u – f
C. v - 1
D. v + 1
D. v + 1
The correct answer is D. v + 1.
The magnification produced by a convex lens of focal length f is given by the formula:
magnification (m) = v/u
where v is the image distance (distance of the image from the lens) and u is the object distance (distance of the object from the lens).
When the object is at infinity (u = ∞), the image distance (v) is equal to the focal length (f).
Therefore,
magnification (m) = v/u = f/∞ = 1/∞ = 0
This means that the image formed by the lens is virtual and at infinity, and the magnification is zero.
When the object distance (u) is finite, the image distance (v) can be calculated using the lens formula:
1/f = 1/v - 1/u
Rearranging the formula, we get:
1/v = 1/f + 1/u
Adding 1 to both sides of the equation, we have:
1/v + 1 = 1/f + 1/u + 1
Which can be written as:
1/v + 1 = (u + f)/(fu) + 1
Now, taking the reciprocal of both sides, we get:
v + 1 = uf/(u + f)
Therefore, the correct answer is D. v + 1, as derived.