# Optics : Diffraction gratings.

• planesinspace
In summary, the conversation is about a question on a diffraction grating from a textbook. The grating has 600 slits per mm and is being used to examine spectral features near a wavelength of 450 nm. The question asks how close the wavelength of two spectral lines can be for them to still be seen as separate peaks. The conversation discusses using equations for diffraction gratings and resolving power to find the answer. The final answer is 3.75x10^-12 m for the difference in wavelength.

#### planesinspace

1. I am attempting a question from a textbook but the wording or perhaps the question itself is confusing me.
*Light falls at perpendicular incidence on a transmission diffraction grating. The second order diffracted light leaving the grating is examined.
The grating has 600 slits per mm, a total width of 10 cm, and is being used to examine spectral features near a wavelength of 450 nm. How close ( in nm) can the wavelength of two spectral lines be, for the two to still be seen as two, rather than blended into a single intensity peak?

## Homework Equations

Ok so I have done question son diffraction gratings before, but all straightforward, and using the equation d*sin theta =m*lamda

## The Attempt at a Solution

i have worked out theta to be 32.6 degrees, and (not sure if this is right) but used the equation for double-slit diffraction: y=m*lamda*D/d and worked out the spacing between the maximum and the first minimum, y, to be 0.05389m. Is this at all on the right track or am I totally lost?

I fear the latter. Any help much appreciated!

I think you want to look up the formulas dealing with resolving power. There is one that gives the resolving power needed to differentiate two close wavelengths in this experiment; and there is another that gives the resolving power of a specific diffraction grating that depends on the order number.

Thanks, i found the equation R=lamda/deltalamda
and R=mN, where N is the number of gratings and m the order.
So i basically worked out R from the second equation where I have both m and N, then I plugged it into the first and got 3.75x10^-12 m for delta lamda, is that on the right track?

That looks right to me.

## 1. What is a diffraction grating?

A diffraction grating is a device used in optics to separate light into its component wavelengths. It consists of a large number of closely spaced parallel lines or grooves etched onto a surface, which act as a series of parallel slits through which light can pass. When light passes through a diffraction grating, it is diffracted in different directions depending on its wavelength, resulting in a spectrum of colors.

## 2. How does a diffraction grating work?

A diffraction grating works by utilizing the principle of diffraction, which is the bending of light waves around an obstacle. When light passes through a diffraction grating, it is diffracted by each individual groove, causing the different wavelengths to spread out and form a spectrum. The spacing between the grooves determines the amount of diffraction and the resulting spectral resolution.

## 3. What is the difference between a transmission and a reflection diffraction grating?

A transmission diffraction grating allows light to pass through the grooves and is typically made of a transparent material such as glass or plastic. A reflection diffraction grating, on the other hand, reflects light off of the grooves and is usually made of a reflective material such as metal. Both types of gratings work on the same principle of diffraction, but have different applications depending on the type of light being used.

## 4. What is the significance of the number of lines per millimeter in a diffraction grating?

The number of lines per millimeter is a measure of the spacing between the grooves on a diffraction grating. This spacing determines the amount of diffraction and the spectral resolution of the grating. A higher number of lines per millimeter means a smaller spacing between the grooves, resulting in a higher spectral resolution and a more detailed spectrum. However, this also means that the diffraction angles are smaller and the intensity of the spectral lines is lower.

## 5. What are the applications of diffraction gratings?

Diffraction gratings have a wide range of applications in various fields such as spectroscopy, astronomy, telecommunications, and laser technology. They are used to analyze the composition of materials, measure the wavelengths of light, and produce laser beams with specific characteristics. They are also used in devices such as spectrometers, monochromators, and optical sensors. Additionally, diffraction gratings are used in everyday objects such as CD and DVD players, where they are used to read the data stored on the discs.

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