The smallest object visible to the unaided
eye is of 100 microns. If you use a
microscope of m=1000, what is the size of
the smallest object you can now see? (So=25cm)
The answer is apparently 100nm. I am still confused as to why. Please help!
To understand why the answer is 100 nm, you need to consider the concept of magnification.
Magnification is the ratio of the apparent size of an object seen through a microscope to its actual size. In this case, the given microscope has a magnification power of m = 1000.
Let's start by finding the apparent size of the smallest object visible to the unaided eye, which is 100 microns (µm). Remember that 1 micrometer is equal to 1 millionth of a meter.
So, the apparent size of the smallest object without magnification is 100 µm.
Now, we can use the magnification formula to find the size of the smallest object when viewed through the microscope:
Magnification = Apparent size / Actual size
Rearranging the formula to solve for the actual size:
Actual size = Apparent size / Magnification
Given that the apparent size (Ao) is 100 µm and the magnification (m) is 1000, we can substitute the values into the formula:
Actual size = 100 µm / 1000
Simplifying the division:
Actual size = 0.1 µm
Finally, we need to convert the actual size from micrometers (µm) to nanometers (nm). There are 1000 nanometers in 1 micrometer.
So, the actual size in nanometers is:
Actual size = 0.1 µm * 1000 nm/µm
Simplifying the multiplication:
Actual size = 100 nm
Therefore, the size of the smallest object you can see through the microscope with a magnification power of m = 1000 is 100 nm.