Physics diffraction problem

Marie uses an old 33-1/3 rpm record as a diffraction grating. She shines a laser, λ = 632.8 nm, on the record as shown in the figure below. On a screen 2.7 m from the record, a series of red dots 14 mm apart are visible.
(a) How many ridges are there in a centimeter along the radius of the record?




(b) Marie checks her results by noting that the ridges represents a song that lasted 4.01 minutes and takes up 16 mm on the record. How many ridges should there be in a centimeter?

d=ridge separation distance
theta=angle of incident with respect to the normal
n= a positive integer = 1
lambda = wavelength = 632.8 nm
D=distance from screen
y=separation distance of maxima = 14 mm

For constructive interference the path length difference between to diffracted been is an integer multiple of the wavelength;

d sin (theta) = n lambda

Since the screen is far away compared to the slit division, we could approximate sin(theta)

sin (theta) = y/D

combine the two above equation to get d=D lambda/y=122 um

A) number of ridges in one centimeter = 1cm/122um = 82

B) Number of revolutions = 4.01 * 33.33 =133.7 rev
Number of revs is directly proportional to the radial length
(133.7)(1 cm/16mm)= 83.5