Calculating Spectrum Width with Diffraction Grating: Helpful Guide

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In summary, The question involves using a diffraction grating with a certain number of lines per cm to calculate the width of the spectrum that appears as the second antinode on a screen that is 100 cm away. The formula for finding the maxima and minima is similar to that of a 2-slit apparatus and involves the distance between the slits, the angle of diffraction, and the wavelength. The displacement of the antinodes on the screen can be determined using geometry and will depend on the wavelength.
  • #1
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:smile:
 
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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.
 
  • #3


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.
 

What is a diffraction grating?

A diffraction grating is a tool used in optics to separate light into its component wavelengths. It consists of a series of closely spaced parallel lines or grooves etched onto a surface, which cause light to diffract and create a spectrum.

How does a diffraction grating work?

When light passes through a diffraction grating, the waves are diffracted (bent) as they interact with the grating's grooves. This causes the light to spread out into its component wavelengths, creating a spectrum. The spacing between the grooves determines the amount of diffraction and the resulting spectrum.

What is the spectrum width?

The spectrum width refers to the range of wavelengths present in a given spectrum. It can be calculated by measuring the distance between the two outermost peaks in the spectrum and converting it to a wavelength range.

How do you calculate spectrum width with a diffraction grating?

To calculate spectrum width with a diffraction grating, you will need to measure the distance between the two outermost peaks in the spectrum using a ruler or caliper. Then, convert this distance to a wavelength range by using the known spacing between the grating's grooves and the formula: Δλ = d sin(θ), where Δλ is the wavelength range, d is the grating spacing, and θ is the diffraction angle.

What is the significance of calculating spectrum width with a diffraction grating?

Calculating spectrum width with a diffraction grating is important in understanding the properties of light and in various applications such as spectroscopy, astronomy, and telecommunications. It allows for the identification and analysis of different wavelengths present in a given light source, providing valuable information about its composition and characteristics.

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