Answer to Question #228134 in Electricity and Magnetism for Arvin Shopon

Question

The wavelength of the school demonstration laser is measured using a grating with 300 slits per millimeter. To this end, a magnet-mounted meter-long ruler is attached to the whiteboard and the laser light is directed perpendicular to the whiteboard. When the grating is placed between the laser and the board 0.79 meters from the board, a light pattern as shown in the figure is detected on the board. Determine the laser wavelength using 2nd order diffraction maxima.

Answer 1

Gives

$e+b=300$ slit per mm

$(e+b)=\frac{10^{-3}}{300}$ m

n=2

D=0.79m

$(e+b)sin\theta=n\lambda$

Second maximum

$\theta=90°\\n=2$

$(e+b)=n\lambda$

$\lambda=\frac{(e+b)}{2}$

Put value

$\lambda=\frac{\frac{10^{-3}}{300}}{2}=\frac{1\times10^{-5}}{6}m$

$\lambda=1666.6nm$