1. OBJECTIVE AND EYEPIECE� The magnifying power of simple microscope can be increased by decreasing the focal length of the lens. However, the focal length of a lens cannot be decreased beyond a certain limit. Moreover, the lens of small focal length has a smaller diameter because the curvature of the surface is large and the field of view is small.� Therefore, to increase the magnifying power, two separate lenses are used. The lens near the object is called the objective. Which forms a real image of an object under examination (Fig. 1).

The lens used to enlarge this image further to form a final image and which is then viewed by the eye is called an eyepiece or

ocular. The objective of an ordinary microscope is usually an achromat with a magnification of about x 5 and an eyepiece usually consists of multiple lenses.

An optical instrument is required to produce a magnified image free from aberrations and a bright image covering a wide field of view. If a single lens is used as an eyepiece, the final image will suffer from spherical and chromatic aberrations. Another drawback is the small field of view, which becomes lesser and lesser as the magnification of the instrument is increased.

The rays passing through the outer portions of the image are refracted through the peripheral portions of the eye lens and they cannot simultaneously enter the small aperture of the pupil of the eye placed close to the eye lens ( Fig. 1). Hence, only that part of the image, which is nearer to the axis, will be seen. Therefore, the final image will cover a small field of view. The field of view will progressively decrease as the distance between the objective and ocular is increased. The distance is varied in order to increase the magnification. In other words, the greater the magnifying power of the instrument, the smaller the field of view.

It becomes therefore expedient to place an additional lens in the eyepiece to cause all the rays from the image to enter the eye lens. This extra lens is called a field lens. The function of the field lens it to gather in more of the rays from the objective toward the axis of the eyepiece

( see Fig. 2). The field lens and the

eye lens together constitute an

ocular or eyepiece. The two lenses

Are made and kept in such a way

that their combination is achromatic

And free from spherical aberrations. Two common eyepieces are the Huygens and the Ramsden types.

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Fig. 2

2. HUYGENS EYEPIECE

In the Huygens eyepiece a converging beam enters the field lens and forms a virtual image before the eye lens. The need for a converging beam implies that this eyepiece does not act like a simple magnifier.

Fig. 1

Construction:

Huygens’ eyepiece consists of two lenses having focal length in the ratio 3:1 and the distance between them is equal to the difference in their focal lengths. The focal lengths and the positions of the two lenses are such that each lens produces an equal deviation of the ray and the system is achromatic. This eyepiece is free from chromatic as well as spherical aberration as if satisfies the two conditions simultaneously.

1. The lens combination acts as an achromatic system if where D is the distance between the lenses and f₁ and f₂ are the focal lengths of the two lenses.
2. The lenses produce equal deviation of the incident ray when the distance between the two lenses are equal to (f₁ – f₂)

The field and the eye lenses used are plano-convex and are placed with their convex surfaces towards the incident ray. In this way, the total deviation due to the combination is divided into four parts which makes the combination to have minimum spherical aberration.

If spherical and chromatic aberrations are to be minimized simultaneously, the following condition it to be satisfied.

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Combining the two conditions, we obtain

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To satisfy the conditions for minimum chromatic and spherical aberrations, the focal length of the field lens should be three times the focal length of the eye lens and the distance between them should be equal to twice the focal length of the eye lens. Huygens’ eyepiece is constructed on this principle.

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Theory :

The objective forms an image, which serves as virtual object for the field lens. The field lens forms real invert image I’I’₁. If this image is situated at the principal focus of the eye lens, then the final image is at infinity.

Equivalent Focal Length :

The equivalent focal length of the eyepiece can be found as follows. If F is the equivalent focal length of the eyepiece, then it is given by

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The equivalent lens lies behind field lens at a distance of

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In other words, the equivalent lens is at a distance of 3f – 2f = f behind the eye lens.

Position of Cross-wires :

It is noted above that the principal focus of the equivalent lens lies f/2 ahead of the eye lens. It is here that the image due to objective must be formed in order that the final image is at infinity. The rays coming from the objective are, however intercepted by the field lens, thus displacing the image to position I₁, It is here that the cross-wire should be placed.

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We further noted above that the image I I₁ is at a distance of f/2 from the eye lens or 3f/2 from the field lens. Hence, for field lens u = -3f/2. Then,

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In other words, I I₁, lies midway between the two lenses and so fixes the position of the cross-wires or scale, if used. Since the image formed by the objective lies behind the field lens (instead of in the front) the eyepiece is sometimes referred to as a negative eyepiece.

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It may be noted that the image of the scale is formed by the eye lens whereas the final image is produced by both the lenses. Hence the image and the scale would not be magnified equally and so the measurement will not be reliable. The image of the cross-wire or scale would have all the defects of an image formed by a single lens. Hence in instruments using Huygens’ eyepieces, scale is not used except when magnification is low.

Merits and Demerits :

(i) The Huygens’ eyepiece is fully free from chromatic aberration because the distance between the lenses is equal to half the sum of their focal lengths.

(ii) Spherical aberration is also minimum because the distance between the two lenses is equal to the difference of their focal lengths.

(iii) the field or view of this eyepiece is smaller than that of Ramsden’s eyepiece.

2.1 CARDINAL POINTS OF HUYGENS EYEPIECE

position of Principal points :

The equivalent lens should be placed at a distance α from the field lens, which is given by

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Since the distance d between the field lens L₁ and the eye lens L₂ is 2f, the position of equivalent lens is 3f - 2f = f, i.e., it should be placed away from the eye lens, as shown by doted line at P₁ in Fig. 1.

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Fig. 2

The first principal point P₁ lies at a distance α = 3f from the field lens. The second principal point P₂ lies at a distance β from the eye lens towards the field lens and is given by

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Position of the Focal Points :

The first focal point F₁ lies at a distance 3f/2 from the first principal point P₁, i. e., at a distance from the eye lens on the side of the field lens.

The second focal point lies at a distance 3f/2 from the second principal point P₂, i.e., at a distance from the eye lens away from the field lens.

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3. RAMSDEN EYEPIECE

Ramsden’s eyepiece consists of two plano-convex lenses each of focal length f separated by a distance equal to (2/3)f. The lenses are kept with their curved surfaces facing each other, as shown in Fig.1, thereby reducing spherical aberration. The field lens is a little larger

than the intermediate

Image and is placed

close to this image to

allow as much light as possible to pass through it. The eye lens has a smaller diameter but carries out the actual magnification.

Fig. 1

Theory :

The objective forms the real inverted image I of a distant object. This serves as an object for the field lens, which gives rise to a virtual image I₁. I₁ in turn serves as an object for the eye lens, which gives the final image at infinity, because I₁ is made to lie at its principal focus.

Equivalent focal length :

The equivalent focal length of the eyepiece can be found as follows. If F denotes the focal length of the equivalent lens, then

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The equivalent lens of focal length 3f/4 must be placed behind the field lens at a distance

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Thus the equivalent lens lies between the field lens and the eye lens.

Position of the cross-wires :

The cross-wires should be placed at the position of I. Now, the position of I relative to field lens can be found as follows. If the final image is to be formed at infinity,

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the image I should lie in the focal plane of the equivalent lens. In other words, the distance AI should be equal to F = 3f/4. Since AL₁ = f/2, I₄ = f/4.

Therefore, the objective should produce the image at a distance of f/4 in front of the field lens. A fine scale may be placed here if it is desired to measure the size of the image. Since the scale and image would be magnified equally, the measurement would be trustworthy.

Merits and Demerits :

1. The field of view of this eyepiece is fairly wide.
2. It is not entirely free from chromatic aberration since the distance between the two lenses is not equal to half the sum of their focal lengths.

However, chromatic aberration is minimised by using an achromatic combination both for the field lens and the eye lens.

(iii) Spherical aberration is minimized by using two plano-convex lenses thereby spreading deviation over four surfaces.

Ramsden’s eyepiece is used practically in all instruments where measurements of the size of the final image are to be made. This eyepiece is sometimes referred to as positive eyepiece because a real image is formed by the objective in front of the field lens, which further acts as a real object for the eye lens.

3.1 CARDINAL POINTS OF RAMSDEN EYEPIECE

Position of the principal planes :

The first principal plane of the equivalent lens lies at P₁ behind the field lens at a distance α given by the relation

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Thus, the equivalent lens is placed at P₁ in between the field lens F and the eye lens E at a distance f/2 behind the field lens, as shown in Fig.2. The point P₁ where the principal plane

cuts the axis is the first

principal point.

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Fig. 2

The second principal plane is at a distance β from the eye lens L₂.

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The second principal plane lies behind the eye lens L₁ at a distance f/2. The point P₂ where the principal plane cuts the axis is the second principal point.

Nodal Points :

As the lens system is situated in air, the nodal points coincide with the principal points. Thus, P₁ and P₂ are the nodal points, N₁ and N₂ respectively.

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Position of Focal Points :

The equivalent focal length of the eyepiece is 3f/4. Hence the first focal point F₁ lies at a distance 3f/4 from the first principal point P₁. That is at a distance of to the left of the field lens L₁.

The second focal point F₂ lies at a distance 3f /4 from the second principal point P₂ i.e., at a distance f/4 behind the eye lens L₂ away from the field lens.

4. COMPARISON OF RAMSDEN EYEPIECE WITH HUYGENS EYEPIECE