You view a mountain with a magnifying glass of focal length 𝑓 equals 10 centimetres. What is the magnification?
Let’s call the magnification we want to solve for capital 𝑀. If we draw a sketch of the scenario, what we have is a magnifying glass between our eye and a mountain off in the distance. We will assume that the distance between the glass and our eye is 25 centimetres, which is known to be an optimal distance for looking for a magnifying glass.
Compared to the distance between our eye and the glass, the distance between the glass and the mountain can be approximated as infinity, which simply means that the light from the mountain comes into the glass moving in parallel rays. With this scenario, the magnification 𝑀 of our glass is equal to the optimal viewing distance 25 centimetres divided by the focal length of our glass 𝑓.
So in our case, 𝑀 equals 25 centimetres divided by 10 centimetres, which gives us a magnification of 2.5 times. So if we were to remove the magnifying glass from between our eye and the mountain, the mountain would look two and half times smaller.