If you are getting a total magnification (TM) of 225X with a 45X high-dry object

Question

If you are getting a total magnification (TM) of 225X with a 45X high-dry objective, what would be the power of the eyepiece (ocular)? For this same 45X high-dry objective, if you knew the NA 0.65, would it be beneficial to use a 15X ocular? Calculate the maximum useful magnification (MUM) and compare it to the TM. In answering this question, show formulas and calculations. Explain the relationship between MUM and TM in determining whether you would get a better image if you increased the power of the ocular for a particular lens. 3.

Explanation / Answer

The total magnification (TM), when using a microscope, can be calculated by multiplying the eyepiece magnification and the objective lense magnification. The eyepiece corresponds to the part of the microscope where you take the look of the specimen; while the objective lens corresponds to the tubes with lenses that are set directly to the specimen slide. Microscopes usually are made with 3 or 4 objective lenses with the next magnifications: 4x, 10x, 40x, and, if there is a fourth lense, 100x. All these means the image gets to be seen 4 times, or 10 times, or 40 times o 100 times bigger.

Just as the objective lense has its magnification written on one side, the eyepiece also has its magnification written on a side, wich usually is 10x.

So, in order to calculate the total magnification (TM) when looking through a microscope, you have to multiply both magnifications from the objective lense and the eyepiece togehter, for example:

When using the objective lense of 40x, you have to multiply: 40 x 10 = 400x. Meaning you are looking the specimen 400 times bigger.

In the question above we are told we have a TM of 225x with a 45x objective lense, and we want to know the power fo the eyepiece lense. This can be calculated as follows: (45) * (x) = 225 -----> 225 / 45 = x ------> 225 / 45 = 5
Therefore the power of the eyepiece lense is 5x.

Now, when observing specimens throuhg a microscope, there is a range of magnification that will allow you to examine different aspects of the specimen. This range is called Useful Maginification, and is set between the minimum maginification needed to start identifying details of an image, and the maximum useful magnification (MUM), where, if we go higher the MUM, the image starts to degrade and details can no longer be examined.
Therefore, we can tell that the useful magnification is the range of magnification where we can examine an specimen, while out of this range we can't get more information.

In order to calculate the useful magnification, we need to know the Numeral Aperture (NA) of the objective lense. This NA corresponds to a value that describes the ability or resolution of an objective, based on a range of angles where light can be emitted and accpeted.  

Once the NA is known, the minimum magnification is arbitrary set as 500 times the NA, while the MUM is set as 1000 times the NA; leading to the next formula:

Useful Maginification = 500x(NA) to 1000x(NA)

This range of values means, your total magnification (TM) has to lay between those values, in order to get a good enought image that can provide us information.

In the case we are working with, they tell us we are using the next values:
Objective Lense: 45x
NA = 0.65

If we calculate the useful magnification we will get the next value:

Useful magnification = 500 (0.65) to 1000 (0.65)
UM = 325 to 650

With an eyepiece lense of 5x we get a TM of 225x (as calculated before), which is a TM that lays within the useful magnification, therefore, a good and useful TM.

But, if we get an eyepiece lense of 15x we will get the next TM:

TM = (15x) * (45x)
TM = 15 x 45
TM = 675

This TM of 675 is higher than 650, leading us to a degraded image no longer useful.

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