I cut my thread to slightly more than one meter in length, so that the spacing between the cards was
L = 100 cm .
I measured the size of the spot of sunlight to be
d = 1.0 cm .
Using these values, I obtain
How accurate is this answer? Using the small-angle formula, you can work out the Sun's true angular size from its distance and diameter, which are given in the book:
Diameter = 1.39 × 106 km ,
Distance = 1.52 × 108 km .
Setting d equal to the Sun's diameter, and L equal to its distance, I get
= 0.52° .
As you see, I over-estimated the angular size of the Sun, but only by about 10%. An uncertainty of about this size is expected since it's hard to measure the diameter of the spot d with an accuracy of better than about 1 mm, or 10%.
You may wonder if the choice of units made a difference. The answer is no, just so long as you use the same units for d and L in the small-angle formula! When you use the same units, d÷L is a pure number, with no units attached. (See the handout on Working With Units for more information).