# A Diffraction Grating Has

Light with a wavelength of about 490 nm is made to pass through a diffraction grating. The angle formed between the path of the incident light and the diffracted light is 9.2° and forms a first-order bright band. What is the number of lines per mm in the diffraction grating? A diffraction grating has 500 lines per mm. Its slit spacing or grating element will be equal to.

## Aim:

1. To determine the number of lines per millimeter of the grating using the green line of the mercury spectrum.
2. To calculate the wavelength of the other prominent lines of mercury by normal incidence method.

## Apparatus

Spectrometer, diffraction grating element and mercury vapor lamp.

## Theory:

When a wave train strikes an obstacle, the light ray will bend at the corners and edges of it, which causes the spreading of light waves into the geometrical shadow of the obstacle. This phenomenon is termed as diffraction. ### Single slit diffraction:

When waves pass through a gap, which is about as wide as the wavelength they spread out into the region beyond the gap. Huygens considered each point along a wave front to be the source of a secondary disturbance that forms a semi-circular wavelet. Diffraction is due to the superposition of such secondary wavelets. The secondary wavelets spread out and overlap each other interfering with each other to form a pattern of maximum and minimum intensity. The pattern formed on a screen consists of a broad central band of light with dark bands on either side. The dark bands are caused when the light from the top half of the slit destructively interferes with the light from the bottom half.

Consider a slit of width ‘a’. Let at an angle θ, the path difference between the top and bottom of the slit is a wavelength. This causes destructive interference to occur because the path difference between the top and the middle of the slit is half of the wavelength. At this angle all the light from the top half of the slit will get cancelled with the light from the bottom half to produce a dark band.

---------------- (1)

Intensity minima will occur if this path length difference is an integer number of wavelengths.

-----------------(2)

Where,

is the order of each minimum
is the wavelength,

is the distance between the slits
is the angle at which destructive interference occurs.

Intensity is given by,

---------------(3)

where is the total phase angle , it can be related to the deviation angle,

---------------(4)

I0 is the maximum intensity λ is the wavelength of the light and a is the slit width.

Diffraction grating is an optical component having a periodic structure which can split and diffract light t several beams travelling in different directions. This depends on the spacing of the grating and the wavelength of the incident light.

At normal incidence,

---------------(5)

where,

N is the number of lines per unit length of the grating

n is the order of the spectrum

is the wavelength of light.

θ is the diffraction angle.

But we can extend the different types of diffraction gratings further to discuss the new and emerging manufacturing techniques for holographic gratings. Etched-in relief gratings comprised of fused silica and volume phase holographic (VPH) diffraction gratings, for instance, are two radically different design paradigms for modern optical systems. While both offer significantly higher efficiency than ruled gratings, VPH grating technology offers the optical engineer more design options to achieve the desired efficiency profile.

#### Selecting a Diffraction Grating

Choosing a diffraction grating comes down to several key interlinked performance factors, including:

• Efficiency: Diffraction grating efficiency is usually expressed as the percentage of incident light converted into the desired order as a function of wavelength, with most conventional gratings yielding asymmetric efficiency curves over the total wavelength range.
• Resolving power: The resolving power of a diffraction grating defines its ability to separate two wavelengths spatially and is determined primarily by the grating’s periodic structure.
• Wavelength range: A diffraction grating’s spectral range concerns the region of electromagnetic radiation that it can effectively disperse, which is likewise characteristic of the structure.

## A Diffraction Grating Has A Point

Wasatch Photonics is one of the industry’s leading suppliers of precision diffraction gratings for various optical systems. We appreciate the challenges of selecting the right optics for your application, and welcome the opportunity to design a grating to your specific needs. If you are looking for a new solution, why not contact us today to explore the possibilities?