What is the relation between the focal length and radius of curvature of a spherical mirror (concave mirror or convex mirror ) ? Calculate the focal length of a sphrical mirror whose radius of curvature is 25 cm.

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One question we receive a lot is about building an IR Illuminator. An IR Illuminator allows a camera to see in total darkness. Infrared light can be useful for security applications, or maybe you want to watch the night activities of the local wildlife.

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To find the relation between the radius of curvature (R) and the focal length (f) of a concave mirror, we can follow these steps:

5. Conclusion: - Therefore, the relation between the radius of curvature and the focal length of a concave mirror is: R=2forf=R2

1. Understand the Definitions: - The focal length (f) of a concave mirror is the distance from the mirror's surface to its focus. - The radius of curvature (R) is the distance from the mirror's surface to the center of curvature, which is the center of the sphere from which the mirror is a part.

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Final Answer:The relation between the radius of curvature (R) and the focal length (f) of a concave mirror is given by:R=2f

3. Relate the Distances: - The distance from the pole (P) to the center of curvature (C) is twice the distance from the pole (P) to the focus (F). This can be expressed mathematically as: R=2f

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The IR Illuminator uses our LED SpotLight PCB, which holds a total of 24 LEDs on a circular PCB. The board contains 24 individual IR LEDs that do all of the work, along with eight current limiting resistors. Assembly time for the kit by a novice builder is about 30 minutes total assembly time.

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The simplest way to begin the install is to insert and solder into the board the inner row of LEDs. These are located at D3, D6, D8, D12, D14, D17, D19, and D22. Keep in mind that LEDs are polarity sensitive, so ensure that you align the flat on the LED with the flat on the solder mask on the board. After you have soldered in the first 8 LEDs, trim the leads.

We have simplified this process with our online Dropping Resistor Calculator. For this build, we are using 390-ohm one-quarter watt resistors.

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We carry both frequencies of the IR LEDs, see our Infrared LED page for models IC601-02 for 850nm and IC401-04 for the 940nm models.

4. Derive the Focal Length: - From the relation R=2f, we can express the focal length in terms of the radius of curvature: f=R2

Now you should install and solder in the LEDs at D1, D2, D4, D5, D7, D9, D10, D11, D13, D15, D16, D18, D20, D21, D22, and D23. When installing the LEDs, try to keep them flat against the board.

2. Visualize the Mirror: - Draw a concave mirror and label the pole (P), focus (F), and center of curvature (C). - The distance from the pole to the focus is the focal length (f), and the distance from the pole to the center of curvature is the radius of curvature (R).

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When you power up your system, you may notice a slight glow to the LEDs. For 850nm LED models, you will see a slight red glow. The 940nm models do not have any glow that is visible to the human eye.

850nm LEDs produce a very slight red glow when operating, which is visible to the human eye. 940nm models produce no visible light to the eye.

What is the relation between focal length and radius of curvature of a concave mirror? Does the same relation hold for a covcave mirror?

When you build your system, you need to decide what frequency of LEDs to install on the board. There are two standard frequencies available, one at 940nm and the other at 850nm. The most commonly used frequency is the 850nm model. Although the 940nm model is more desired for covert operations.

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Once assembled, the power to the circuit is needed. We have set up this unit to run on 12v DC at about 160mA (0.160A). To operate at other voltages, you must select the correct value of a dropping resistor (of which there are eight).

Once you have all the parts, the first step is to become familiar with the PCB. It is set up with 24 LEDs in total, 18 around the outside, and another 8 on the inside (the LEDs are labeled D1 to D24). Resistors go on the board at positions R1 to R8, which are between the inner and outer rows of LEDs. Finally, apply power to the board just below D24, where you will see the Positive and Negative solder pads. In the very center of the PCB is a single hole. The hole can be enlarged for mounting or even further to fit around a camera lens.

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The last step is for the installation of the eight current limiting resistors which go at positions R1 to R8. The resistors will stand on their ends for this project. Unlike the LEDs, the resistors are not polarity sensitive to install any way you want.