Question

4. (12 points) Monochromatic light of wavelength 640 mm is directed at normal incidence through a grating having 6000 lines per centimeter onto a screen 2.60 m away. a. Find the distance between consecutive slits on the grating. b. Find the distance on the screen between the central maximum and the first order maximum.

Answer 1

(a) $d=\frac{L}{N}=\frac{10^{-2}}{6000}=1.67\times 10^{-6}m^{-1}$

(b)

(b)

from the image above:

$tg\vartheta =\frac{x}{l}\approx sin\vartheta$

(form small angles of diffraction)

In the case of normal incidence (i=0):

$dsin\vartheta =k\lambda$

k=the order of diffraction

$sin\vartheta =\frac{k\lambda}{d}$

Using the 2 formula one obtains:

$\frac{x}{l} =\frac{k\lambda}{d}$

$x =\frac{kl\lambda}{d}$

Replace the numerical values and get the distance between the central maximum and the first order maximum.

Appendix: A zoom for the first part of this image: