Determination of the angular resolving power of the eye.
A. Study of relations of the angular resolving power of the eye from illumination.
I. Course of the exercise.
1. Connect the test set for the research, which is placed at the optical bench to the transformer’s terminals “0” and “12V” to illuminate it.
2. Fix the autotransformer's lever with millimeter scales in position 190 or 195, when the illumination of the test is optimal.
3. Take the place of the shield, watching the test set through sight-glass.
4. Dim lighting in the room.
5. Select one of the three tests (eg, 3 or 4th, depending on the individual characteristics of the eye) by a distance of good vision (d). This distance corresponds to that position on the test bench, in which the vertical and horizontal lines of the test are seen clearly.
6. Connect the test set to the transformer terminals "0" and "6V" allowing the use of weaker lighting.
7. Turn off the light in the room.
8. The autotransformer’s lever set in such a position that the observer could see clearly only the first test (other tests should be invisible or blurry).
9. Read the position of the upper edge of the autotransformer’s lever (SA). When reading- illuminate only the scale of the autotransformer, not directing light to the observer.
10. For the resulting position of the autotransformer‘s lever read "IgE" from the attached diagram.
11. Repeat activities 8, 9, 10 for subsequent tests 2, 3, ..., 9 noting the distance between dashes "a". The results put in the measuring table.
Lp. / SA / Log E / a [mm] / a [rad] / a [min] / [min-1]II. Computational informations.
1. Calculate the angles a using the fact that for small angles: tgα @ α = a/d, where
a - the mutual distance of two points seen yet separately
d - distance of the object from the nodal point of the eye
The angles, obtained in this way, are expressed in radians. To convert it to degrees, and then to minutes, use the following proportion:
2. Calculate the angular resolving power of the eye from the formula:
wherein a a in minutes. Put the results in a table.
3. Plot a graph of Z = f (IgE).
4. Discuss the results and draw conclusions.
B. Examination of angular resolving power of the eye depending on the distance.
I. Course of the exercise.
1. Set the test at a maximum distance from the eye and illuminate in that way to observator was able to see separately and sharp only test 1. Read the test’s position on the optical bench (d1).
2. Move closer set of tests so that tests 1 and 2 were seen separately and sharp. Read the position on the optical bench (d2).
3. Move closer set of tests so that tests 3, 4, ..., 9 were seen separately and sharp. Read the position on the optical bench (d3, …,d9). The results of the measurements put in the measuring table.
L.p / d [mm] / a [mm] / a [rad] / a [min] / [min-1]II. Computational informations.
1. Calculate the angular resolving power of the eye from the formula:
wherein a is in minutes. The results put in a table (like in the point A).
2. Plot a graph of Z = f (d).
3. Discuss the results and draw conclusions.
Measurement of the resolving power and useful magnification of optical’s microscope
I. Course of the exercise.
1. Set measuring disc under the objective. Looking through microscope set the sharp vision of spots placed on the upper surface of the testing disc.
2. Remove the eyepiece and testing disc and put the graph paper in place of the testing disc.
3. Looking at the scale through the tube (without eyepiece) count the number of divisions of graph paper falling within the field of view.
4. Repeat the measurement for three other discs.
5. For the next two objectives repeat activities 1 – 4.
II. Computational informations.
1. Calculate the aperture’s angle from the formula:
where m is the width of the field of view, h is the disc thickness.
From the tangent of the aperture’s angle calculate the same angle and its sine. The results place in the measuring table.
I / 12.00
12.12
12.75
13.00
II
III
2. Calculate the numerical aperture from the formula:
A = n sin u
For each objective calculate the average value of aperture.
3. For each objective calculate the microscope’s resolving power from the formula:
assuming the wavelength λ = 0.55 mm. The results put in the following table.
Objective number / Z[m-1] / Pus / Pus,eyI
II
III
4. With limited resolving power of the microscope is related the so-called useful (optimal) magnification of microscope:
Pus = 1000 A
In practice, it is not worth using in the microscope magnifications greater than the useful magnification because they do not allow see any further details of the watching preparation. For each objective calculate the useful magnification of the microscope. The results put in the table.
5. Because the total magnification of microscope is equal to the product of the objective and the eyepiece magnification, so knowing useful magnification of microscopy we can choose the optimum (useful) value of the magnification of the eyepiece:
According to the above formula calculate, for each objective, the useful magnification of the eyepiece. The results put in the table.