Working of Human Eye and Simple Microscope

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.