Diffraction grating, lines per mm, and how to show the spacing

[Sharr-zeor]

A diffraction grating is labelled 300 lines mm^-1 (lines per mm)
Show that the spacing (d) between the lines on the grating is 3.3 x 10^-6m



i can't really think of any relevant equations. but I'm assuming standard form. i can't believe that the answer would be as simple as converting to m's from mm's



since there are 300 lines in every mm, i assumed converting to standard for, and metres instead of mm. which might get me close to the answer.

300 lines per mm = 3000 per cm = 3000000 per m = each line 3 x 10^-6 ?

this isn't right, clearly. since the anser is 3.3 x 10^-6, i just can't work out how to show it

 

[Pyroadept]

300 lines per mm is equivalent to 3x10^5 lines per m (mulitply by 1000).
Therefore, the distance between two lines is 1/(3x10^5) = 3.333...x10^6


Think of it in simple terms: If there are two lines per metre on a grid, then the distance between two lines must be 0.5 m (i.e. 1/2)

 

[nlightner]

mathematically.



I can explain the concept of diffraction grating and how to show the spacing between the lines using the given information of 300 lines per mm.

A diffraction grating is a device that contains a large number of parallel and equidistant lines that are used to diffract light. The spacing between these lines, denoted as d, plays a crucial role in determining the diffraction pattern produced by the grating.

In this case, the diffraction grating is labelled as 300 lines per mm, which means that there are 300 lines in every millimeter. To determine the spacing between these lines, we need to convert the units to a common form. Since the given spacing is in millimeters, we can convert it to meters by dividing it by 1000.

So, 300 lines per mm is equivalent to 0.3 lines per mm. Now, we can use the formula d = 1/n, where n is the number of lines per unit length. In this case, n = 0.3 lines per mm. Therefore, the spacing between the lines on the grating is:

d = 1/n = 1/0.3 lines per mm = 3.3 x 10^-6 m

This shows that the spacing between the lines on the diffraction grating is 3.3 x 10^-6 m, which matches the given answer. This calculation can be further verified by using a ruler to measure the distance between the lines on the grating, which should be approximately 3.3 micrometers.

In conclusion, the spacing between the lines on a diffraction grating can be determined by using the formula d = 1/n, where n is the number of lines per unit length. By converting the units to a common form, we can easily calculate the spacing between the lines and show it mathematically.