What is the space between two consecutive grooves on the CD

[thuanthuan]

Stand a couple of meters from a lightbulb.
Facing away from the light,
hold a compact disc about 10 cm
from your eye and tilt it until the reflection
of the bulb is located in the
hole at the disc’s center. You should
see spectra radiating out from the
center, with violet on the inside and
red on the outside. Now move the
disc away from your eye until the violet
band is at the outer edge. Carefully
measure the distance from your
eye to the center of the disc and also
determine the radius of the disc. Use
this information to find the angle a to
the first-order maximum for violet
light. Now use Equation 38.10 to determine
the spacing between the
grooves on the disc. The industry
standard is 1.6
m. How close did
you come?

( Fundamentals of Physics, p1226, 7th edition)

Can you tell me how to perform this experiment ? .. and also prove that it's true.
I don't understand it.
Thank you.

 

[thuanthuan]

note that equation 3.10: for diffraction grating, the condition for maxima in the interference pattern at the angle a is d.sina=m.lambda
(d = slit spacing. m=0,1,2... - order number, lambda=wavelength)