Ramsden's Eye-piece

Ramsden’s Eye-piece

It consist of two plano-convex lens having equal focal length seperated one-another by the distance of \(\frac{2}{3}f\). The convex surface are exposed towards each other.

(i) Spherical aberration:

The system is said to be free from the spherical aberration if, seperation between lenses is zero i.e. d = \(f_1 – f_2\)

= f – f = 0 not equal to \(\frac{2}{3}f\).

Therefore, the spherical aberration exist, so, it removed by using suitable combination of lenses.

(ii) Chromatic Aberration:

The system is said to be from chromatic aberration, if seperation between the lenses (d) = \(\frac{f_1 + f_2}{d}\)

i.e. \(\frac{f_1 + f_2}{2} = \frac{f + f}{2} = f\), which is not equal to d.

therefore, the chromatic aberration exist and it is removed by achromatic combination of lenses.

(iii) Combined focal length:

The combined focal length of two plano-convex lens seperated by distance d is;

$$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1f_2}$$

$$=\frac{1}{f}+\frac{1}{f}-\frac{\frac{2}{3}f}{f^2}$$

$$=\frac{2-\frac{2}{3}}{f}$$

$$=\frac{4}{3f}$$

$$\therefore\;\;F=\frac{3}{4}f$$

(iv) Position of final image:

Here, \(II_1\) is the real position of object for field lens and it produced a virtual magnified image at \(I’I’_1\). This virtual image is used as an object for eye-lens and it produces magnified image at infinity.

(v) Position of cross-wire:

The cross-wire system is used for the quantitatative measurement of the magnified final image. In the case of Radamen’s eye-piece, the cross-wire can be placed at the initial position of the object i.e. \(II_1\). Therefore, cross-wire and object both are magnified by field lens and eye-lens in equal proportion. Therefore, cross-wire system can be used for the mathematical measurement of magnified image in Ramsden’s eye-piece.

(vi) Cardinal point:

In the development of various optical formulae, the effect of thickness is neglected. But, in the system of combination of lenses, the thickness becomes significant and hence the effect of thickness should be included in the development of optical formulae. The combined system of lenses can be explained by considering a single unit under the help of following point which are called cardinal point.

(1). Principle point:

a) First principle point: First principle point (\(H_1\))from field lens (\(L_1\)) is at $$L_1H_1=\frac{Fd}{f_2}$$

$$=\frac{\frac{3}{4}f.\frac{2}{3}f}{f}$$

$$=\frac{f}{2}$$

1. b) Second principle point: i.e. \(L_2H_2\) from eye lens (\(L_2\)) is at

$$L_2H_2= -\frac{Fd}{f_1}$$

$$=\frac{-\frac{3}{4}f.\frac{2}{3}f}{f}$$

$$=-\frac{f}{2}$$

i.e., at a distance \(\frac{f}{2}\) left from eye lens.

(2). Focal points:

1. a) First focal point: $$L_1F_1=-F\biggl(1-\frac{d}{f_2}\biggr)$$

$$=\frac{-3}{2}f\biggl(1-\frac{\frac{2}{3}f}{f}\biggr)=\frac{-f}{4}$$

So, it lies at \(\frac{f}{4}\) distance left from field lens.

1. b) Second focal point: $$L_2F_2=F\biggl(1-\frac{d}{f_1}\biggr)$$

$$=\frac{3}{4}f\biggl(1-\frac{\frac{2}{3}f}{f}\biggr)=\frac{f}{4}$$

So, it lies at \(\frac{f}{4}\) distance right from eye lens.

(3). Nodal point:

In the case of Ramsden’s eye-piece, the lenses \(L_1\) and \(L_2\) are placed at the same medium, so the nodal points coincide with the prnciple axis. And the position of these cardinal points in Ramsden’s eye-piece has been shown in the diagram above.

Points in Ramsden’s Eye-piece:

1. Cross-wire can be used because the image formed bythe objective lies in front of the field lens.
2. The condition for minimizing spherical aberration is not satisfied.
3. It does not satisfy the condition for achromatism.
4. It is achromatic for only two choosen colours.
5. The other types of aberration are better eliminate.
6. The eye clearence is good.
7. It is used for quantitative purposes in microscopes and telescopes.
8. Its power is positive.
9. The two principle planes are crossed.
10. it can be used as a simple microscope. This is because the first principle planes lies to the left of the lens and the focal planes are real.
11. The nodal points coincides with the principle points.

References:

Adhikari, P.B, Daya Nidhi Chhatkuli and Iswar Prasad Koirala. A Textbook of Physics. Vol. II. Kathmandu: Sukunda Pustak Bhawan, 2012.

Jenkins, F.A and H.E White. Fundamental of optics. New York (USA): McGraw-Hill Book Co, 1976.

wood, R.W. Physical Optics. New York (USA): Dover Publication , 1934.