A magnifier has a magnification of 6x. How far from the lens should an object be held so that its image is at the near point distance of 25 cm?
I tried doing the problem by using the equation M = 25cm / f.
M = 25 cm/6 = 4.17 cm
However when I put the answer into mastering physics, it says that the answer is incorrect. I was wondering if anyone could tell me what am I doing wrong.
To correctly solve this problem, you need to use the correct formula for calculating the distance between the lens and the object in a magnifying system. The formula is given by:
1/f = 1/v - 1/u
Where:
- f is the focal length of the magnifier
- v is the distance of the image from the lens
- u is the distance of the object from the lens
In this case, the magnification (M) is given by:
M = v/u
We are given that the magnification (M) is 6x and the near point distance (v) is 25 cm. We need to find the distance (u) from the lens to the object.
To start solving this problem, let's manipulate the magnification formula to isolate the image distance (v):
M = v/u
v = M * u
Now, substitute the given values into the equation:
25 cm = 6 * u
Divide both sides of the equation by 6:
u ≈ 4.17 cm
So, the correct answer is indeed approximately 4.17 cm. The problem may lie elsewhere, such as rounding errors or a different mistake in the calculations. Make sure you are using the correct units and carefully check any numerical calculations or any additional quantities in the problem that may affect the result.