today I will finally continue to write about optics. Last time I was talking about dioptre and today I will explain how magnifier and microscope works.
Angle of view
Angle of view plays important part in magnifier, microscope and so on. The problem why we can not see individual cells in leaf with naked eye is that we are not able to distinquish things that are too close to each other. Human eye is able to distinquish things that are about 1′ (arc minute=1/60° degrees) apart.
You can easily try it when you draw something on paper and then walk away from it. Or you are not able to tell trees apart when you are hundreds meters away from them.
(On the picture you can see the angle of view for camera, it can be measure horizontaly, verticaly or diagonally).
To make this angle bigger so we can distinquish everything we can walk towards stuff. But when we have a leaf we can get only limitely close to its surface and our eye can not adjust to something so close. Look at your thumb when you put it three centimeters from your nose. It will be blurry even if you try your best, this is because your eye does not have enough dioptre to make the image clear, plus your eye is going to hurt because of the muscles in eye stretching to make the optical power of your eye bigger. Conventional visual distance is distance for which human eye has to release least effort, this is about 25 centimeters.
To know the distance two objects must be apart to distinquish them we can use tangens:
τ is the angle of view which is for human 1′.
y is the distance of two objects which you are trying to distinquish.
d is the distance from you to the objects.
y=d * tg τ
So the limit of our eye is that it is not able to be powerful enough so we need something which will help us and it has to work the same way as our eye, magnifier!
The light rays are going too much away from each other and your eye is not able to change their direction to create picture.
There is thing called angular magnification.
γ=τ’/τ = tg τ’/tg τ = y/f/y/d = d/f
γ is the angular magnification and f is the distance to focal point.
Angular magnification says to us how much our magnifier is strong. The formula above works for objects that are right in focal point, otherwise there would be “a” which is the distance to the object. If the object is right in focal point our eye does not need anything to do and as it gets closer the light rays are more and more going apart so that at one point you will need better magnifier and then it just wont be enough so you will have to use microscope.
There are two lenses in microscope. The first one is close to the object and it has the largest dioptre possible, making its focal point small as possible. It is called objective lens.
The second one is not so strong and its role is to make finally adjustment of light rays so they create image in your eye.
The picture above which I drew is horrible wrong but I can describe what is going on there. On the right you have the small object (brown). There is light coming from it in all various angle but important is that the lens has enough dioptres to use them all. F’ is the focal point of second lens, this point should be at the distance where all the rays from first lens converge into one point but I was not able to draw it properly. This is the way microscope is designed. Those rays start to go apart again but soon they hit the second lens, converging again and entering the eye in proper angles so that they hit all the spots on red line creating much bigger image.
Microscope is not unlimited source of magnification since when you will try to make bigger something too small you will get into problem with the wavelength of light.