The powder technique utilizing a strip of film as described in the figure below is called the Debye$-$

Scherrer method and the camera which holds the film and sample a Debye$-$Scherrer camera.

Take the radius of the camera as $R$ and derive an equation

relating the distance between the lines produced by a cone

of $x-$rays diffracted from an $\{hkl\}$ set $($S on the above

picture$)$ and the $$ value for that $\{hkl\}$ set.

A Debye$-$Scherrer pattern is made of $Cu$ powder using a

camera with a $5cm$ radius and $Cu{K}_1$ radiation

$(=0\mathrm{.}1541nm).$ Make a sketch of the film pattern similar

to that shown above locating the first order diffraction

lines from those planes listed in Table $2\mathrm{.}1.$ Give the value

of $S$ for each line$-$pair appearing on the film. The lattice

parameter of $Cu$ is $0\mathrm{.}3615nm.$

$R=5cm,=0\mathrm{.}1541nm,R=0\mathrm{.}3615cm$

Locate the second order lines and give their $S$ values.

Table $2\mathrm{.}1$ Indices of the Reflecting Planes for Cubic Structures