GRE Subject Test: Physics - Diffraction

A beam of light, with wavelength $400\textup{ nm}$ , is normally incident on a transmission diffraction grating. With respect to the incident beam, the first order diffraction maximum occurs at an angle of $6^\circ$ . What is the number of slits per centimeter on the grating?

$2.5*10^3\ \frac{\textup{lines}}{\textup{cm}}$

$2.5*10^5\ \frac{\textup{lines}}{\textup{cm}}$

$4*10^6\ \frac{\textup{lines}}{\textup{cm}}$

$4*10^4\ \frac{\textup{lines}}{\textup{cm}}$

$4*10^5\ \frac{\textup{lines}}{\textup{cm}}$

Explanation

The equation describing maxima of a diffraction grating is:

$d\sin(\theta)=m\theta$

Where d is the separation of slits, which can also be expressed as:

$d=\frac{L}{N}$

Substituting d into the first equation and making the small angle approximation, one can solve for $\frac{N}{L}$ (lines per length):

$\frac{N}{L}=\frac{\theta}{m\lambda}=\frac{0.1}{1\times 400\times 10^{-9}}=2.5\times 10^5\ \frac{\textup{lines}}{\textup{m}}$

Note that the angle had to be converted from degrees to radians. Finally, the question asks for lines per centimeter, not meter, so the answer becomes $2.5*10^3\ \frac{\textup{lines}}{\textup{cm}}$ .

Diffraction

Help Questions

Explanation