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Ques. Draw a labelled ray diagram of a compound microscope. Why are the objective and the eye-piece chosen to have a small focal length? (CBSE 2013)(2 marks)

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Ans. Magnifying power of a compound microscope is defined as “the angle subtended at the eye by the image to the angle subtended (at the unaided eye) by the object”.

Ques. Why must both the objective and the eyepiece of a compound microscope have short focal lengths? (CBSE 2017)(2 marks)

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Many laser scanning systems for material processing today are based on galvanometer-actuated mirror systems and utilize fiber lasers for efficient and fast engraving on metals. However, galvanometers (and fiber lasers) are expensive and complicated to drive.

Ans. For getting higher magnification in compound microscope, both objective and eyepiece must have short focal length, because

Ques. A compound microscope uses an objective lens of focal length 4 cm and eyepiece lens of focal length 10 cm. An object is placed at 6 cm from the objective lens. Calculate the magnifying power of the compound microscope. Also calculate the length of the microscope. (CBSE 2011)(3 marks)

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An object of size 3.0 cm is placed 14cm in front of a concave lens of focal length 21cm. Describe the image produced by the lens. What happens if the object is moved further away from the lens?

A quick note: Scanning in this context does not refer to the digitalization of a physical 3D-Object. It refers instead to the process of engraving by moving the laser spot line by line.

Simple Microscope is used at a very basic level, where there is no meticulous requirement for research. It comprises a single lens. It is an instrument that gives a large image of a minute object. It produces an erect virtual image of the object. It has a double convex lens with a short focal length.

In a parallel plate capacitor with air between the plates, each plate has an area of 6 × 10–3 m2 and the distance between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor?

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From this paper I was able to rearrange some formulas to know the direct relation of XY-movement and necessary mirror rotation (See my Prototype report for more details).

Ques. How does the power of a convex lens vary, if the incident red light is replaced by violet light? (Delhi 2008)(2 marks)

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This projects goal is to create a similar system using stepper motors, which are very simple to use, and a cheap laser diode (= 650nm) to simulate the fiber laser beam. It also acts as a prototype for an engraver using this kinematic but with a high power diode laser.

Ques. Define the magnifying power of a compound microscope when the final image is formed at infinity. Why must both the objective and the eyepiece of a compound microscope have short focal lengths? Explain. (CBSE 2016)(2 marks)

The electronics of the scanner are relatively simple as well. At the heart of the system lies a Teensy 4.0 chosen due to its incredibly high clockspeed of 600MHz and above (a normal Arduino Uno only has 16MHz!). It controls the motor via two SilentStepStick TMC2209 stepper motor drivers, reads the endstops for the mirrors and controls the laser diode (7mW 650nm ADL65075TA4) using a transistor. For controlling the current of the laser diode, a cheap universal laser driver is chosen. The whole package is fed 12V input voltage with a LM317 supplying 5V for the Teensy Board. The power of the laser diode can be adjusted by turning a potentiometer.

The general mechanics of the scanner could not be simpler: Two stepper motors with attached mirrors (I used 20mm CO2-Laser mirrors because I had them laying around), two endswitches and the 3D-printed base to hold it all together. The optics, in general, are pretty simple as well: The laser diode itself is seated in a brass housing contained in an aluminium block acting as a heatsink. The brass housing also contains a collimator lens so that the beam is parallel (=collimated). The beam exits the housing and gets deflected by the mirrors. Of course, the machine must know exactly how much the mirrors need to be turned for a specific position on the target plane (XY-coordinates are given by G-Code commands). Luckily, I was able to find a paper describing the mathematical model of this exact kinematic (Link).

I wont go too much into detail of the code since this is the most boring part for most people, but the general structure of the software can be seen in the figure above. By the way, all of the code can be found on the GitHub-Page of the project. The basic instructions are stored as G-Code (e.g. G0 X10 Y10) in a .txt file. These commands are transmitted line by line to the Teensy by a Python via USB. The Firmware interprets the lines and rotates the mirrors accordingly. This can be done at very high speeds (due to the high clock frequency of the Teensy), resulting in a smooth movement of the laser dot.

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This test is done at various speeds, from 3000 to 20000 steps/s (distance 200mm). As you can see, the higher the speed, the smoother the projection looks. However above ~ 15k steps/s mechanical vibrations and motor limits are quite noticable.

Ques. You are given two converging lenses of focal lengths 1.25 cm and 5 cm to design a compound microscope. If it is desired to have a magnification of 30, find out the separation between the objective and the eyepiece. (CBSE 2014)(3 marks)

Difference between simple and compound microscopes lies in the fact that compound microscopes have a much stronger magnifying capacity and are used in intense research. Some of the other microscopes are the stereo, inverted, metallurgical and polarising microscopes.

A compound microscope is usually also referred to as a Biological Microscope. The parts of a Compound Microscope include:

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Ans. Definition of resolving power: Resolving power of compound microscope is defined as the reciprocal of the smallest distance between two point objects at which they can be just resolved when seen through microscope.

Ans. A compound microscope consists of two convex lenses coaxially separated by some distance. The lens nearer to the object is called the objective. The lens through which the final image is viewed is called the eyepiece. The focal length of objective lens is smaller than eyepiece

A very detailled Prototype Report for this system can be found at my GitHub-Page. This report is written like a scientific paper and should give a lot more insight into the design details of the project.

Ans. Epi-Fluorescence, stereo microscopes, Phase contrast microscope, Polarizing, Reflected light Metallurgical, Differential Interference microscope, and Brightfield Transmitted Microscope.

All in all, the system behaves surprisingly well considering what it is made of. I also did some quite extensive accuracy tests, see chapter 4.2 of the Prototype report, but they are generally of little concern in this application.

I hope you enjoyed reading this short summary of the project! I really enjoyed working out all of the little details of the machine and really suggest reading the Prototype Report linked above. It does go into detail quite a bit more than this article! The successor of this prototype, a 5W “galvo” laser engraver using this kinematic approach actually is already functional. Hopefully I’ll have found the time to write an article about it by the time you are reading this!

Ans. Firstly, the object gives a magnified image of the object and after that the eyepiece produces the angular magnification.

The purpose of a compound microscope is similar to a simple microscope. It uses multiple lenses to magnify real-world objects that are microscopic to the naked eye. It is used for professional purposes where intense research is required. It comprises a plane mirror surface on one side and a concave mirror surface on the other side. Compound microscopes have multiple lenses.