Human eye
Human eye is a natural optical instrument. The human eye is
shaped like double convex lens having a refractive index close to 1.437. It is
fixed in its place with the help of the muscles. It has the ability to change
the focal length while seeing near and distant objects. The unique feature of
automatic adjustment of focusing is called power of accommodation.
The nearest a distance for a human eye is 25 cm and it is
called least distance of distant vision. The far point is infinity.
The angle that an object subtends at the eye is called visual
angle. Microscope and telescopes are designed to increase the visual angle and
hence increase the apparent size of the image.
With respect to the increase of the age, the near point
gradually increases.
Myopia means near point is fine for a human eye but the Far
Point turns finite instead of infinite. It is also called the short sight.
Long sight means the far distant objects appears fine but near
distant object is unable to be seen properly. It is simply because the near
point for the particular eye is more than 25 cm. It happens because the final
images formed behind the retina.
The long sight and the short sight can be corrected with the help
of the proper lenses.
Simple microscope
It is a simple convex lens which is used to see the magnified
image of an object. With the help of this is simple microscope we can increase
the visual angle as well as the size of the image. This process is called
magnification and the simple instrument is called simple microscope. This is
also called as magnifying glass or reading glass.
The object is placed before the convex lens and the
corresponding image also shall be seen in the same direction. This is possible
only when the object is placed at between the principal focus of the convex
lens. If the object is placed at the principal focus of the lens, the final
images formed at infinity. This kind of adjustment is called relaxed eye
adjustment and in this case the magnification is going to be less.
If the object is placed within the principal focus and the
final images formed at a finite point and we will be getting a better
magnification. Anyway as the image is at a finite point to observe that image,
our eyes will be strained a little bit more and that’s why this position is
called strained position.
If the light of higher wavelength is used, its focal length
is more and hence its magnification will be less.
The simple microscope is having a limitation of producing a
better magnification up to only four times the size of the object. If we try to
get better magnification above that four times, the image consists of
aberrations. That is why, we prefer to use it only to produce a magnification
that is less than the four times the size of the object.
If we are in need of the magnification more than this, we
shall use a device called compound microscope.
Problem and solution
The image attached below is having two problems. Solving the
first problem is a simple task. We need to calculate the power of the lens and
we know that the power is nothing but the reciprocal of the focal length of the
lens. We can also calculate the magnification of the lens as the ratio of image
distance of distant vision to the focal length of the lens. Similarly using the
formula we can also calculate the focal length for the strained eye as shown in
the diagram.
The second problem needs a little bit of analysis. Let us try
to first give the problem and then give you the analysis.
Problem
A man with the normal near point reads a book with the small
print using a magnifying glass of focal length 5 cm. What are the closest and
the farthest distance at which he can read the book when viewing through the
glass?
What are the maximum and minimum magnifying powers for this
gas?
Solution
We have to use the lens formula with proper sign convention
to solve this problem. For the object distance to be minimum, the corresponding
image also shall be minimum location. For the object distance to be maximum,
the corresponding image can be at infinity. Taking these points into
consideration, we can solve the problem as shown below.
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