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Showing posts with the label Maths

How to build your own telescope

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Learning about lenses , refraction and optics in general has now enabled me to make my own telescope. I wanted to build one because I have always loved space and astronomy. Another day I must tell you about a hobby of mine, launching water rockets.  There are two main types of telescopes: refractors (made out of lenses) and reflectors (use mirrors too). Galileo Galilei made one of the first refractor telescopes and Isaac Newton made the first reflector. The one I built is a refractor, which is a bit cheaper to build.  How it works In this diagram you can see that the telescope has two lenses: The first is called the "objective". The function of the objective is to create an image with the light comes from the celestial body. The light rays come in parallel because the object is very far away. This means the image forms in the focal point. The image is inverted though. The second lens is called the "eyepiece" and it typically has a much smaller focal length. The eye...

Snell's Law

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In the previous blog post I talked briefly about Snell's law, however, I couldn't cover this topic due to the fact that I did not know the maths required. Guess what! I know them now. Well, at least at a basic level. Let's get into it. The thing I needed to learn was the "sine" of an angle. The cool thing is that in a right-angle triangle, like the one below, if you take one side of the right-angle ("a" below) and divide it by the opposite side of the right-angle ("h" below) then you get same number no matter what size the triangle is.  As you can see a1/h1 is 0.708 and so is a2/h2 almost perfectly. This number is called the sine of the angle O1. By the way "h" is called the hypotenuse ... who came up with that name! I have learnt how to work with a table of sines to calculate the sine of an angle. I use this one from NASA . So, now we can understand Snell's law. It predicts how much the light will bend when it changes media based...

Conic sections with Tinkercad

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During science week I saw a conference from an astrophysicist showing us photos of stars. He told us what a reflector telescope is and how it uses a parabolic mirror. So I asked my dad about parabolas and he told me about the conic sections. Conic sections are different shapes you get by cutting a cone at different angles. I decided to see this by myself using Tinkercad. You can find other posts in the blog talking about Tinkercad if you are interested. It is very easy to use. These are all the sections I created When you cut a cone horizontally you get a circle. Here we have represented the circle in yellow. If you cut a little bit more inclined than horizontal you get an ellipse. Here you can see three different ellipses at different angles in red colour and how the first one compares with the circle. The more you incline the cut, the stretchier it gets. Ellipses are cool because that's the type of orbit planets do around the Sun If you keep inclining the cut eventually you reach...

Practicing times tables

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In this blogpost I will tell you about a program I made so that anyone can practice times tables for free. In order to learn the times tables you need someone to ask you random questions but if your parents/carers are busy, this program will never say "I am busy". When you click the green flag the ghost glides on to stage and will ask you 20 random questions. It will tell you if your answer is correct. If you get it wrong it tells you the right answer. However, it doesn't keep track of how many questions you get right or wrong so that you don't get upset. The important thing is to practice often and not to let your mistakes make you sad. By default it will ask you 20 questions from all times tables between 2 and 9. If you have an account in Scratch you can modify it to suit your needs. The important code is in these 3 lines For example, what if want to get 30 questions and only practice the 7 times tables? You can change the code like this. You can access the program ...