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

Answer:

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

Explanation:

we know that fringe width is given as

$y = \frac{\lambda D}{d}$

where

$\lambda  = 650 nm$

D = 1.2

for CD first order fringe 2yi = 98 cm

y1 = 49 cm = 0.49 m

so,$d_1 = \frac{650\times 10^{-9} \times 1.2}{0.49} = 1.891 \times 10^{-6} m$

$d_1 = 1.591 \times 10^{-3} mm$

Number of line on Cd per mm is $N_1 = \frac{1}{d_1} = 628.2$lines per mm

for DVD

first order fringe 2y2 = 210 cm

y1 = 105 cm = 1.05 m

so, $d_2 = \frac{650\times 10^{-9} \times 1.2}{1.05} = 7.428 \times 10^{-7} m$

$d_2 = 7.428 \times 10^{-4} mm$

Number of line on Cd per mm is $N_2 = \frac{1}{d_2} = 1346.2$ lines per mm

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