Calculating Spectrum Width with Diffraction Grating: Helpful Guide

[Velocity]

This question really has me stumped..i would appreciate it if anyone could help me out

White light containing wavelengths of 400nm to 750 nm is shone normally onto a diffraction grating of 3000 lines/cm. Calculate the width of the spectrum that appears as the second antinode on a screen that is 100 cm away.

Is there a specific formula I can use to solve the question? If so then please help.. thanks

 

[quantumdude]

The condition for maxima/minima is the same as that of a 2-slit apparatus. For adjacent slits separated by a distance d, we must have:

dsinθ=mλ for maxima and
dsinθ=(m+1/2)λ for minima.

In both cases, m is an integer.

You use the information given about the grating to determine d and you use geometry to determine the displacement y of the antinodes on the screen. Note that your expression for y will depend on the wavelength λ.

 

[M98Ranger]

Yes, there is a specific formula that can be used to solve this question. The formula is:

Spectrum Width = (distance between adjacent maxima) x (number of lines on grating)

First, we need to calculate the distance between adjacent maxima. This can be done using the formula:

Distance between adjacent maxima = wavelength / (number of lines on grating x order of maxima)

In this case, the order of maxima is 2 (since we are looking for the second antinode). So, the distance between adjacent maxima can be calculated as:

Distance between adjacent maxima = 750 nm / (3000 lines/cm x 2) = 0.125 cm

Now, we can plug this value into the first formula to calculate the spectrum width:

Spectrum Width = (0.125 cm) x (3000 lines/cm) = 375 cm

So, the spectrum width that appears as the second antinode on the screen 100 cm away is 375 cm.