Microscope and Telescope

Microscope:

A simple magnifier or microscope is a converging lens of small focal length is shown in the figure. In order to use such a lens as a microscope, the lens is held

near the object, one focal length away or less, and the eye is positioned close to the lens on the other side.

The idea is to get an erect, magnified and virtual image of the object at a distance so that it can be viewed comfortably, i.e., at 25 cm or more. If the object is at a distance f, the image is at infinity. However, if the object is at a distance

slightly less than the focal length of the lens, the image is virtual and closer than infinity.

Although the closest comfortable distance for viewing the image is when it is at the near point (distance D @ 25 cm), it causes some strain on the eye.

Therefore, the image formed at infinity is often considered most suitable for viewing by the relaxed eye. This is shown in the below figure.

The linear magnification m, for the image formed at the near point D, by a simple microscope can be obtained by using the relation

Now according to our sign convention, v is negative, and is equal in magnitude to D. Thus, the magnification is

------ (i)

A simple microscope: the magnifying lens is located such that the image is at the near point

A simple microscope: the angle subtanded by the object, is the same as that at the near point

A simple microscope: the object near the focal point of the lens; the image is far off but closer than infinity

Note that where h is the size of the object and is the size of the image. The angle subtended is then given by

------ (ii)

We now find the angle subtended at the eye by the image when the object is at u. From the relations

we have the angle subtended by the image as

The angle subtended by the object, when it is at u = –f

------ (iii)

The angular magnification is, therefore

------ (iv)

For larger magnifications, one uses two lenses, one compounding the effect of the other. This is known as a compound microscope. The ray diagram is shown below.

The lens nearest the object, called the objective, forms a real, inverted, magnified image of the object. This serves as the object for the second lens, the eyepiece, which functions essentially like a simple microscope or magnifier, produces the final image, which is enlarged and virtual.

The first inverted image is thus near (at or within) the focal plane of the eyepiece, at a distance appropriate for final image formation at infinity, or a little closer for image formation at the near point. Clearly, the final image is inverted with respect to the original object.

The magnification is due to a compound microscope which shows that the (linear) magnification due to the objective, namely , equals

------ (v)

Where we have used the result,

Where is the size of the first image, the object size being h and f_o being the focal length of the objective. The first image is formed near the focal point of the eyepiece.

The distance L, i.e., the distance between the second focal point of the objective and the first focal point of the eyepiece (focal length fe) is called the tube length of the compound microscope.

The final image is formed at the near point, is

------ (vi - a)

When the final image is formed at infinity, the angular magnification is

------ (vi – b)

Thus, the total magnification when the image is formed at infinity, is

------ (vii)

In modern microscopes, multicomponent lenses are used for both the objective and the eyepiece to improve image quality by minimising various optical aberrations (defects) in lenses.

Telescope:

The telescope is used to provide angular magnification of distant objects. It also has an objective and an eyepiece. Light from a distant object enters the objective and a real image is formed in the tube at its second focal point.

The eyepiece magnifies this image producing a final inverted image. The magnifying power m is the ratio of the angle b subtended at the eye by the final image to the angle a which the object subtends at the lens or the eye. Hence

In this case, the length of the telescope tube is

Terrestrial telescopes have, in addition, a pair of inverting lenses to make the final image erect. Refracting telescopes can be used both for terrestrial and astronomical observations.

For example, consider a telescope whose objective has a focal length of 100 cm and the eyepiece a focal length of 1 cm. The magnifying power of this telescope is m = = 100.

Let us consider a pair of stars of actual separation 1′ (one minute of arc). The stars appear as though they are separated by an angle of 100 × 1′ = 100′ =1.67°

The main considerations with an astronomical telescope are its light gathering power and its resolution or resolving power. The former clearly depends on the area of the objective. With larger diameters, fainter objects can be observed.

The resolving power, or the ability to observe two objects distinctly, which are in very nearly the same direction, also depends on the diameter of the objective. So, the desirable aim in optical telescopes is to make them with objective of large diameter.

The largest lens objective in use has a diameter of 40 inch (~1.02 m). It is at the Yerkes Observatory in Wisconsin, USA. Such big lenses tend to be very heavy and therefore, difficult to make and support by their edges. Further, it is rather difficult and expensive to make such large sized lenses which form images that are free from any kind of chromatic aberration and distortions.

Schematic diagram of a reflecting telescope (Cassegrain)

For these reasons, modern telescopes use a concave mirror rather than a lens for the objective. Telescopes with mirror objectives are called reflecting telescopes.

There is no chromatic aberration in a mirror. Mechanical support is much less of a problem since a mirror weighs much less than a lens of equivalent optical quality, and can be supported over its entire back surface, not just over its rim.

One obvious problem with a reflecting telescope is that the objective mirror focusses light inside the telescope tube. It has the advantages of a large focal length in a short telescope.

The largest telescope in India is in Kavalur, Tamil Nadu. It is a 2.34 m diameter reflecting telescope (Cassegrain). It was ground, polished, set up, and is being used by the Indian Institute of Astrophysics, Bangalore. The largest reflecting telescopes in the world are the pair of Keck telescopes in Hawaii, USA, with a reflector of 10 metre in diameter.