A convex lens of focal length
f, forms a real image whose size is the same as that of the object.
The object distance is equal
A. 4F
B. 2F
C. F
D. F/2
E. F/4
The correct answer is C. F.
The magnification of a convex lens is given by the formula:
magnification (m) = (-) image distance (i) / object distance (o)
In this case, since the size of the image is the same as that of the object, the magnification is equal to 1. Therefore:
1 = (-) i / o
Since the object distance is equal to the focal length of the lens (o = f), we can substitute this into the equation:
1 = (-) i / f
Rearranging the equation, we get:
i = (-) f
This means that the image distance is equal to the negative value of the focal length. In other words, the real image is formed on the opposite side of the lens compared to the object, and its distance is equal to the focal length.
Therefore, the object distance is equal to the focal length, or option C. F.
To solve this problem, we can use the lens formula:
1/f = 1/v - 1/u
Where:
f = focal length of the lens
v = image distance from the lens
u = object distance from the lens
Given that the real image formed by the convex lens is of the same size as the object, this means that the magnification (M) is equal to 1:
M = v/u = 1
From the lens formula, we can substitute v/u = 1:
1/f = 1/1 - 1/u
1/f = 1 - 1/u
Now, we need to find the value of u when the image distance is equal to the object distance. Let's substitute v=u:
1/f = 1 - 1/u
To make the equation simpler, let's multiply both sides by u:
u/f = u - 1
Let's rearrange the equation:
u - u/f = 1
u(1 - 1/f) = 1
Now, divide both sides by (1 - 1/f) to solve for u:
u = 1/(1 - 1/f)
To find the value of u, we need to simplify this expression:
u = f/(f - 1)
Since we know that the object distance, u, is equal to f/(f - 1), we can determine the answer by comparing this expression to the given options.
Comparing u = f/(f - 1) to the options:
A. 4F is not equal to f/(f - 1)
B. 2F is not equal to f/(f - 1)
C. F is not equal to f/(f - 1)
D. F/2 is equal to f/(f - 1)
E. F/4 is not equal to f/(f - 1)
Therefore, the correct answer is option D. F/2.