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The diagram shows the path of a light ray through a triangular prism. What is the sum of the angles 𝑎 and 𝑏?

In this question, we need to work out the sum of these two angles, 𝑎 and 𝑏. We can see that both 𝑎 and 𝑏 are angles between one surface of the prism and one of these dashed lines. Recall that these dashed lines are called normals. When we draw ray diagrams like this, we often draw normal lines to help us visualize the path of the light correctly. Crucially, normals are always drawn normal to the surface of the prism that the light is passing through.

Remember that normal just means perpendicular to. This means that the angle between each normal and the corresponding surface of the prism is simply 90 degrees. Hence, both 𝑎 and 𝑏 are equal to 90 degrees. So, the sum of 𝑎 and 𝑏 is just 90 degrees plus 90 degrees. This works out as 180 degrees. The sum of the angles 𝑎 and 𝑏 is 180 degrees.

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