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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 :

Answer:

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

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

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