The focal length of the lens of the camera is 1/4 meter, and Sarah is 1/2 meter from the camera lens. What is the distance of the image from the lens?
1/f = 1/o + 1/i
1/(1/4) = 1/(1/2) + 1/i
4 = 2 + 1/i
i = 2
Well, well, well, looks like Sarah is getting her close-up! Now, let's see, if the focal length of the lens is 1/4 meter and Sarah is 1/2 meter away, we might need to focus our attention on the equation known as the lens formula.
The lens formula goes like this: 1/f = 1/v - 1/u, where f is the focal length, v is the distance of the image from the lens, and u is the distance of the object from the lens.
Now, plugging in the values we have, 1/(1/4) = 1/v - 1/(1/2). Let's put our math hats on and calculate this little equation. Simplifying, we get 4 = 1/v - 2.
Okay, let's bring all the Vs on one side and give them a little group hug. Adding 2 to both sides gives us 6 = 1/v. Now, to fully embrace the idea of the distance of the image from the lens, we take the reciprocal of both sides. So, v = 1/6.
Voila! The distance of the image from the lens is 1/6 meter. Keep striking those poses, Sarah!
To calculate the distance of the image from the lens, you can use the lens equation:
1/f = 1/di + 1/do
Where:
- f is the focal length of the lens
- di is the distance of the image from the lens (what we're trying to find)
- do is the distance of the object from the lens (given as 1/2 meter)
Plugging in the given values, we have:
1/(1/4) = 1/di + 1/(1/2)
Simplifying the equation:
4 = 1/di + 2
Subtracting 2 from both sides:
2 = 1/di
Taking the reciprocal of both sides:
di = 1/2
Therefore, the distance of the image from the lens is 1/2 meter.
To find the distance of the image from the lens, we can use the lens formula:
1/f = 1/u + 1/v
Where:
- f is the focal length of the lens
- u is the distance of the object from the lens
- v is the distance of the image from the lens
Given:
- The focal length of the lens is 1/4 meter, so f = 1/4
- Sarah is 1/2 meter from the camera lens, so u = 1/2
Plugging these values into the formula, we have:
1/(1/4) = 1/(1/2) + 1/v
Simplifying, we get:
4 = 2 + 1/v
Subtracting 2 from both sides, we have:
2 = 1/v
Taking the reciprocal of both sides, we get:
v = 1/2
Therefore, the distance of the image from the lens is 1/2 meter.