Question

The shiny surface of a CD is imprinted with millions of tiny pits, arranged in a pattern of thousands of essentially concentric circles that act like a reflection grating when light shines on them. You decide to determine the distance between those circles by aiming a laser pointer (with λ = 680 nm) perpendicular to the disk and measuring the diffraction pattern reflected onto a screen 1.5 m from the disk. The central bright spot you expected to see is blocked by the laser pointer itself. You do find two other bright spots separated by 1.4 m, one on either side of the missing central spot. The rest of the pattern is apparently diffracted at angles too great to show on your screen. What is the distance between the circles on the CD’s surface?

Answer 1

By using the diffraction pattern created by laser light reflecting off a CD, and applying the equation relating the groove spacing to the fringe pattern, you are able to calculate the groove spacing on the CD's surface.

Step-by-step explanation:

To determine the distance between the circular patterns on a CD's surface, also referred to as groove spacing, we can utilize the diffraction pattern created when a laser beam is reflected off the surface. Given the laser wavelength (λ) and the diffraction pattern on the wall, we can apply the equation d sin θ = mλ, where d is the groove spacing, θ is the diffraction angle, m is the order number of the fringe, and λ is the wavelength of the laser light.

To find the angle θ, we observe the first-order fringe (m=1) which is 0.700 meters from the central maximum on one side. The path length from the CD to the wall is 1.50 meters. Using the tangent function, we have tan θ = opposite/adjacent = 0.700 m / 1.50 m. Assuming small angles, where tan θ ≈ sin θ, we can solve for d. For a laser with λ = 680 nm, the fringe separation d on the CD can be calculated.

Answer 2

Distance between two concentric circles is in radius d = 1.0 um

Step-by-step explanation:

Given:

- Wavelength of light λ = 680 nm

- Distance of disc from screen x = 1.5 m

- Separation between central and first order y = 1.4 m

- Angle Q is between central order and mth order

Find:

What is the distance between the circles on the CD’s surface? - d?

Solution:

- The relationship between and wavelength and the position of fringes with respect to diffraction grating is given by Youns's experiment as follows:

sin (Q) = m*λ / d

- Compute the angle Q for first order m = 1:

sin(Q) = 1.4 / sqrt(1.4^2 + 1.5^2)

sin(Q) = 1.4 / 2.05183

sin(Q) = 0.68232

- Use the above result and compute for the grating d for m =1 :

d = λ / sin(Q)

d = 680*10^-9 / 0.68232

d = 1.0 um

- Since the circles are concentric the difference in radius is d = 1.0 um