Q1.
Now close one eye and show a thumbs up with your outstretched hand towards your friend as shown in Fig. 12.12. Are you able to cover the entire head of your friend with your thumb?
Answer
Yes — with one eye closed and the arm stretched out, the thumb completely hides the head of a friend standing about 5 metres away, even though the thumb is far smaller than the head.
| Object | Actual size | Distance from your eye | Apparent size |
|---|---|---|---|
| Your thumb | About 2 cm wide | About 60 cm | Roughly the same as the head's |
| Friend's head | About 16 cm wide | About 500 cm (5 m) | Roughly the same as the thumb's |
thumb: 2 cm at 60 cm → 2 ÷ 60 ≈ 0.033
head: 16 cm at 500 cm → 16 ÷ 500 ≈ 0.032
The two ratios are nearly equal, so the two apparent sizes are nearly equal.
head: 16 cm at 500 cm → 16 ÷ 500 ≈ 0.032
The two ratios are nearly equal, so the two apparent sizes are nearly equal.
Why it happens: the size an object seems to have — its apparent size — depends on its actual physical size and on how far it is from you. A small object held close can match a large object far away.
This is the whole secret of a solar eclipse: the Sun is about 400 times wider than the Moon, but it is also about 400 times farther away. So both look almost exactly the same size in our sky, and the Moon — the "thumb" — can hide the Sun completely.