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 × 10^{6} km ,

*Distance* = 1.52 × 10^{8} 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).

Joshua E. Barnes (barnes@ifa.hawaii.edu) Last modified: September 17, 1999