Focal length

"Good news, Herr Mendel," the glass cutter Rosenstrauch told his friend much later that same evening. "I have succeeded in putting your microscope back together. I think you should test it."

True to his promise, once the repairs were complete, Herr Rosenstrauch had sent a messenger to the monastery to so inform Brother Gregory. Not wanting to wait, the monk had left his evening meal early, and made his way back into town. He found the glass shop closed, but a knock on the door had gained him quick admittance.

"Most of the damage was to the barrel of the microscope," Herr Rosenstrauch said, pointing at the somewhat battered metal part of the instrument that connected the main sets of lenses. "The hardest part of the repair was making sure that the objective and eyepiece lenses were on the same axis, and their focal planes were parallel."

Mendel picked up the microscope and looked at it carefully. It still showed signs of its recent ordeal, but the dents had been hammered out, and when he tested the focusing mechanism, it moved smoothly and evenly. "Thank you," he said. "Do you have any slides on which I could test it?"

"Not really," the glass cutter told him, "it is not my field of expertise. But take it back to the monastery, try it out, and let me know what you think." He picked up the box of extra lenses Mendel had brought with him on his first visit. "But these are still giving me a problem. None of them are labeled so I have no idea what is their focal length or degree of magnification."

Mendel explained that they were a random collection of lenses he had either been given by Abbot Napp, Brother Matthew, or by his friends at University. Lenses, being expensive, were valuable gifts, but he had never tried to use most of them, not knowing their properties.

"I think I can devise a way of testing them," Rosenstrauch said thoughtfully, putting down the box and picking up one of the small, oak drawers that lined one wall of his workshop. "Look here."

Inside the drawer Brother Gregory saw a series of single lenses all wrapped in fine paper and marked on the outside with a series of letters and numbers. Rosenstrauch poked around and then selected two or three specimens. "Let's see," he said, putting down the drawer and returning to the table and the optical bench.

"All lenses have three properties that interest us; the type of glass from which they are made, their focal length and their degree of magnification. Using this simple method, we can find out at least two of these properties." He put down his selection of lenses, and reconfigured the optical bench for his demonstration.

At one end of the marble topped bench, Rosenstrauch once again set up a strong light and masked off most of it so a diffuse glow provided general illumination, which he directed at right angles to the first clamp and bar. The bar, made of metal and triangular in shape, ran the whole length of the bench. In the first clamp, near the light, Rosenstrauch placed a shiny metal pin with a large head.

"This is our 'object'," he told Mendel. He then placed a second clamp and holder about half way along the metal bar, and in the holder placed one of the lenses from the draw. Then he moved to the far end of the triangular bar, placed yet a third clamp and holder, but in this one he put an eye piece.

"We now adjust them, so," he said, moving the lens closer to the 'object', and turning the holder so that the axis of the lens was in the same plane as the bar. He then moved the eyepiece towards the lens and object. "We are ready," he said.

Dutifully, for he had seen similar demonstrations before, Mendel moved to the optical bench and held the shiny metal ruler that would be used later to make the measurements. "What kind of lens is this?" he asked, taping the lens holder with a finger.

"A thin, convex lens," he was told. "They are the simplest for this kind of demonstration. Rosenstrauch was very happy, it was rare that he got someone to share his hobby and his passion, and even more rare that it was someone like Herr Mendel. "Watch, I place the object, the pin, all the way at the end of the bar, like this. I place the lens in the middle of the bench, and the eyepiece thus. Now look through the eyepiece. Tell me what you see."

As he had expected, Brother Gregory saw the image of a tiny steel pin. "But what does it look like?" Rosenstrauch wanted to know. "Describe it to me."

"It certainly looks smaller that the real object - the pin," said Mendel, pointing at the illuminated pin at the far end of the bench. "And it is upside down."

"Inverted," exclaimed Rosenstrauch, happily. "The image is smaller than the object and is inverted. This is what happens when the object is far from the lens, and outside the distance known as the focal length. Now, I adjust the relationship between the lens and the object, so, and now what do you see?"

What Mendel had seen was his friend moving the object closer to the lens, but he had also seen that the distance was very carefully chosen, so he was not surprised when he looked through the eyepiece and saw the image of the pin, still inverted, but this time the same size as the object. All of which he told Rosenstrauch.

"This is a special position. The object is exactly the same size as the image at this distance from the lens, but," he once again adjusted the relationship of the lens and the object. "If we move the object closer to the lens - look - now what do you see?"

It was no surprise to Brother Gregory when the pin was closer to the lens the image was larger than the object.

"It was 'magnified' wasn't it?" Rosenstrauch wanted to know, and was grinning when his prediction was confirmed. "And now, watch. Look through the eyepiece, and tell me to stop when the image changes again." He gently pushed the clamp and the pin along the metal bar and Brother Gregory saw through the eyepiece, the image of the pin got larger and larger then, in an instant, suddenly vanished to be replaced by a swirling blur. "Stop!" he exclaimed.

"The image is no longer a sharp one of the pin, it is dispersed and well - impossible to see," he said.

"That is because the object is exactly one focal length away from the lens. It is at the 'focal point' of this lens. Use that ruler you are holding, and measure how far the pin is from the center of the lens."

This proved to be more difficult than Mendel had imagined, but he finally succeeded, and holding his thumb nail on the ruler, read out the result. "Twenty five centimeters."

"I don't know why we have to use this metric rubbish," Rosenstrauch grumbled. "But I suppose you are used to it from University." He picked up the piece of paper in which the lens had been wrapped and read the numbers. "About 42% of a Klafter, that is correct," he admitted. "That is the first property of a lens. Now, let's see what happens when ---"

But Brother Gregory stopped him. "Please forgive me Herr Rosenstrauch, but it is getting late and I must return to the monastery. I have to get up early in the morning - classes, you know. It is a school day and my students will expect me to be alert." He grinned. "But I've enjoyed our little experiment, and thank you for helping me with the microscope." He picked it up. "I'll test it right away and let you know how it works. We can continue this analysis of the lenses at that time."

With great reluctance, Rosenstrauch let his friend go, and locked up the shop after him. But he did not go at once to his bed. There was still the matter of the speed of light to solve, and he felt that he was getting close.