How to draw an optically correct diagram in a book

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

21 October 2018

There was a public outcry recently about the contents of a primary school text book that appeared to idolise politicians’ showmanship – landing a helicopter in a school and with three big cars waiting to carry him away.

The book elicited so much anger among commentators in the internet social media that the publisher – Jomo Kenyatta Foundation (JKF) – to recall it for revision of the offending content.

A few days before the story of the JKF book broke out, I had posted a picture taken from the Moran Publishers Secondary Atlas. It showed an illustration of how the tilting of the earth causes the seasons.

However, the diagram showed the sun as a smaller object than the earth. The reality is that the diameter of the sun is over 100 times that of the earth. Unfortunately, this error in the atlas did not elicit any emotional reaction from the public. Consequently, it did not get much publicity and it continues to be used by pupils.

Nevertheless, some of the few people who replied to my post were of the opinion that the atlas was correct! This was surprising: it was proof of the danger that such errors pose – children grow up believing in the mistakes.

Others pointed out that it would be impossible to draw the diagram to the correct scale showing the sun 100 times the size of the earth. This is somewhat true; but the aim the figure is to show how the sun’s rays strike the earth.

To serve that purpose, the diagram only needs to be “optically correct”. That is, the angles in the figure must be equal to those in the real situation. At this point, it is important to emphasise that, when an image is magnified, its lengths change but the angles do not.

For a diagram showing how rays of sunlight land on the earths surface, the important angle is the one between the two lines joining the poles of the planet to the poles of the sun, respectively.

That is; think of a line running from the north pole of the earth to the north pole of the sun and another one from the southern tip of the planet to the southern end of the sun. What is the angle between these two lines?

To find the answer, we need just two measurements: the diameter of the sun and it distance from earth. These are approximately 1.4 million kilometers and 150 million km, respectively. With these two values, secondary school pupils should be able to calculate the desired angle.

The answer comes to approximately half a degree. That’s a very small angle. It is so small that it would not be discernible across the page of a regular book.

In other words, if diagram illustrating how sunlight arrives on the earth is to be “optically correct”, then both the planet and the sun should be of the same diameter. That way, the rays of light will be seen striking the earth at the same angles as they do in real life.