Question

The reflective surface of a CD consists of spirals of equally spaced grooves. If you shine a laser pointer on a CD, each groove reflects circular waves that look exactly like the circular waves transmitted by the slits in a grating. You shine a green laser pointer (λ = 532 nm) perpendicularly to the surface of a CD and observe a diffraction pattern on a screen that is 3.0 m away from the CD. You observe that the 1st order maximum (m = 1) appears 1.1 m away from the central maximum (m = 1).
Determine the distance between the adjacent grooves on a CD.

Answer 1

Answer:

d = 1.55 * 10⁻⁶ m

Explanation:

To calculate the distance between the adjacent grooves of the CD, use the formula, $d = \frac{m \lambda}{sin(A_{m}) }$..........(1)

The fringe number, m = 1 since it is a first order maximum

The wavelength of the green laser pointer, $\lambda$ = 532 nm = 532 * 10⁻⁹ m

Distance between the central maximum and the first order maximum = 1.1 m

Distance between the screen and the CD = 3 m

$A_{m}$ = Angle between the incident light and the diffracted light

From the setup shown in the attachment, it is a right angled triangle in which

$sin(A_{m}) = \frac{opposite}{Hypotenuse} \\sin(A_{m}) =\frac{1.1}{\sqrt{1.1^{2}+3^{2}}}$

$sin(A_{m} ) = 0.344\\A_{m} = sin^{-1} 0.344\\A_{m} = 20.14^{0}$

Putting all appropriate values into equation (1)

$d = \frac{1* 532*10^{-9} }{0.344 }\\d = 0.00000155 m\\d = 1.55 * 10^{-6} m$