Question

You shine a blu-ray beam (405 nm) directly at the back of a CD. You notice several reflections at different angles: 0 degrees, 14.3 degrees, 29.7 degrees, 48.0 degrees, and 82.0 degrees. If you shone a different beam (780 nm) at the same CD, what angles of reflection would you see?

Please explain how you solved the question

Answer 1

The grooves on the back of a CD can be considered as a diffraction grating.

The diffraction grating formula for angular locations of maxima is $d\sin\theta=n\lambda$

where is distance between successive lines of grating, $\lambda$ is wave length of light, is order of maximum.

For blu-ray beam $\lambda_1=405\,nm$

angles of maxima for different orders are

For
2
$\theta_1=0\degree$

For $n=1$

-1 식-14.30 64 sın

For
2

64 sın 1SIn

For $n=3$

Άλι (41-48.0 64 sın 1SIn

For $n=4$

(20 64 sın 1SIn

For a different wavelength $\lambda_2=780\,nm$

$d\sin\theta_2=n\lambda_2$

For
2
$\theta_2=0\degree$

For $n=1$

$d\sin\theta_2=\lambda_2$ and $d\sin\theta_1=\lambda_1$

$\theta_2=\sin^{-1}\left(\frac{\lambda_2}{d} \right )=\sin^{-1}\left(\frac{\lambda_2\sin\theta_1}{\lambda_1} \right )=\sin^{-1}\left(\frac{\lambda_2\sin14.3\degree}{\lambda_1} \right )=28.4\degree$

Similarly

For

2

$d\sin\theta_2=2\lambda_2$ and $d\sin\theta_1=2\lambda_1$

$\theta_2=\sin^{-1}\left(\frac{2\lambda_2}{d} \right )=\sin^{-1}\left(\frac{\lambda_2\sin\theta_1}{\lambda_1} \right )=\sin^{-1}\left(\frac{\lambda_2\sin29.7\degree}{\lambda_1} \right )=72.6\degree$

For $n=3$ and $n=4$

reflection maxima do not exist for $\lambda_2=780\,nm$