Most of our blood cells contain a red coloured protein called haemoglobin. This is what binds with oxygen molecules, enabling the blood to do its job of carrying oxygen from your lungs to the rest of the body. Why is haemoglobin itself red? It all comes down to the chemical structure of its molecules, and how they interact with light.
Each colour of light can be thought of as a wave of energy vibrating at a particular speed, or frequency. Specific molecules will soak up energy at some frequencies but not others: shine white light (which contains all the colours) onto haemoglobin and it absorbs all the colours apart from red, which is reflected back to your eyes.
Interestingly, deoxygenated blood returning to the lungs through your veins is a much darker red than the oxygenated blood that leaves via your arteries. This is because the oxygen bonds with the haemoglobin, altering its structure and making it absorb some of the red light, too.
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