Question

CDs and DVDs act effectively like diffraction gratings when reflecting laser light. Holding the disks 1.2 from a wall, you notice that the difference between the two = 1 bright fringes is 98 for the CD and 210 for the DVD when red laser light ( = 650 ) is reflected. How many more lines per mm does a DVD have than a CD?

Answer 1

718 lines per mm is number of line which are more in DVD than CD

Step-by-step explanation:

we know that fringe width is given as

`y = (\lambda D)/(d)`

where

`\lambda  = 650 nm`

D = 1.2

for CD first order fringe 2yi = 98 cm

y1 = 49 cm = 0.49 m

so,
`d_1 = (650* 10^(-9) * 1.2)/(0.49) = 1.891 * 10^(-6) m`

`d_1 = 1.591 * 10^(-3) mm`

Number of line on Cd per mm is
`N_1 = (1)/(d_1) = 628.2`lines per mm

for DVD

first order fringe 2y2 = 210 cm

y1 = 105 cm = 1.05 m

so,
`d_2 = (650* 10^(-9) * 1.2)/(1.05) = 7.428 * 10^(-7) m`

`d_2 = 7.428 * 10^(-4) mm`

Number of line on Cd per mm is
`N_2 = (1)/(d_2) = 1346.2` lines per mm

N_2 -N_1 = 1346.2 - 628.2 = 718 lines per mm