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Nodal Slide

Experimental determination of nodal points: The experiment is based on the following facts:

1. A beam of parallel rays after refraction through the system converges to a point which is situated on the second focal plane.

2. An incident ray directed towards the first nodal point, after refraction through the system, proceeds from the second nodal point in a parallel direction.

3. When the system is rotated slightly about a transverse axis passing through the second focal plane remains stationary.

4. When the media on both sides of the system are the same, the principal coincide with the nodal points.

Suppose a beam of parallel rays is incident on the optical system whose nodal points are N₁ and N₂. After refraction the emergent beam converges to the second focus F₂ and a real image I is formed on the screen. If the system is rotated about a transverse axis through O which lies between N₂ and F₂, N₁ and N₂ take new positions N₁’ and N₂’. A ray incident at N₁’ and directed towards the first nodal point N₁ takes the path N₂’ I1 such that N₂’I₁ is parallel to the incident ray. Since the incident beam is parallel the image must lie on the second focal plane.

Consequently I₁, the point of intersection of the ray N₂’I₁ with the focal plane, is the new position of the image. Thus when the axis of rotation lies between N₂and F₂, a slight rotation of the system in any direction moves the image in the opposite direction.

Next, suppose the system is rotated by a small angle about a transverse axis through N₂. Then N₁ takes its new position N₁’, while N₁ remains fixed. Consequently the position of the parallel emergent ray N₂I is unchanged and the image remains stationary at I.

If the axis of rotation passes through a point O₂ which is away from N₂, then a slight rotation of the system displaces both N₁ and N₂. A ray AN₁’ directed towards N₁’ takes the path N₂’I₂ and the new position of the image is I₂.

Thus, when the axis of rotation is away from N₂, a slight rotation of the system in any direction displaces the image in the same direction. In this way the position of the axis of rotation, for which there is no displacement of the image can be easily found. The intersection of the principal axis with this position of the axis locates the position of the second nodal point. The media on the both sides of the system being the same, the nodal points coincide with the principal points and consequently the distance between the screen and the axis of rotation gives the focal length of the system.

To locate the nodal points, the lens system is mounted with its axis horizontal on a carriage which can be rotated about a vertical axis and can be moved longitudinally with the help of a rack and pinion arrangement. This apparatus is known as nodal slide.

The nodal slide is clamped in front of a screen provided with an illuminated slit fitted with cross wires. On the other side remote from the screen is mounted a vertical plane mirror. The distance between the screen and the lens system is adjusted in such a way that a well that a well defined image of the slit is obtained on the screen adjacent to it. Obviously, the centre of the slit is at the first principal focus of the system. The carriage i snow rotated through a small angle and it will be found that the image shifts sidewards to the right or to the left. The carriage and the upright (stand) carrying the nodal slide are then adjusted such that the direction of rotation of the image changes its sign and finally the image remains stationary for a slight rotation of the carriage. The distances between the screen and the axis of rotation for no shift in image measures the first principal focal length of the lens system. The other focal length can be determined by turning the nodal slide through 180˚ and repeating the experiment.