Diffraction Grating Formula
Diffraction Grating Formula
Making several parallel scratches on the surface of a flat piece of transparent material results in a Diffraction Grating Formula. The material can have a lot of scratches applied to it per square centimetre. The grating that will be utilised, for instance, has 6,000 lines per cm on it. Although the scratches are opaque, the spaces between them allow light to pass through. When light strikes a diffraction grating, it multiplies for the source with parallel slits. A student will learn the Diffraction Grating Formula with examples through the article published on the Extramarks website and mobile application.
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Diffraction Grating Formula
The rays will fall in a parallel bundle on the grating. The wavefront will be perpendicular to the rays and parallel to the grating since the rays and wavefront constitute an orthogonal set. In this case, Huygens’ Principle is relevant.
According to this theory, each transparent slit turns into a new source, and every point on a wavefront acts as a new source, causing a cylindrical wavefront to extend from each.
The waves cancel and there is no light when a peak constantly touches a valley. Additionally, the light is significantly brighter at that place if peaks frequently follow valleys and vice versa. Diffraction is an alternative method to using a prism to observe spectra.
The notes and solutions for the Diffraction Grating Formula are also made available in Hindi for students of various other boards. Comprehension of the Diffraction Grating Formula is made easier with the help of these notes, thanks to Extramarks experts. The notes and solutions based on the Diffraction Grating Formula have been prepared in accordance with the NCERT Syllabus, emulating the structure of the NCERT books.
Concept of the diffraction grating
Take into account two rays that form an angle with a straight line as they emerge. If the difference between their two path lengths is an integral multiple of their wavelength, or in other words, if there is constructive interference,
Now, n 𝜆=𝑑𝑠𝑖𝑛(𝜃)
n = 1, 2, 3, etc.
The Diffraction Grating Formula is what this is.
The angle of emergence at which a wavelength will be bright is denoted by the symbol in this expression. d is also the separation between slits. Obviously,
The notes and solutions based on the Diffraction Grating Formula have been curated by Extramarks experts after great consideration and research on the past years’ question papers. The framework of the Diffraction Grating Formula notes designed by Extramarks experts is very easy to understand and comprehend. The Diffraction Grating Formula notes are extremely internet compatible, and students can also download them for offline study and reference.
The formula for diffraction grating:
N is the grating constant and represents the number of lines per unit length, hence d = 1N. Additionally, the positive integer n is the order of the grating, which represents the recurrence of the spectrum.
Additionally, a complete spectrum for n = 1 and another for n = 2, etc., could be seen, but at larger angles.
The notes and solutions based on the Diffraction Grating Formula have been compiled by some of the top subject-matter experts working in collaboration with Extramarks to make learning easier and fun for students.
The Diffraction Grating Formula notes and solutions are extremely student-friendly, dynamic, diverse and varied in nature. Experts make sure that the notes are updated according to the CBSE NCERT syllabus and pertain to the framework of the NCERT books.
The Hindi version of the Diffraction Grating Formula notes and solutions has been compiled by some of the most skilled translators at Extramarks. The Diffraction Grating Formula solutions can be used by students to take personal notes.
Below is an overview of the kind of examples that have been presented with reference to the Diffraction Grating Formula provided by Extramarks.
Solved Examples
Q.1: Light is diffracted at 20 by a diffraction grating. If there are 1000 lines per millimetre of grating length, what will the wavelength of the light be?
Solution:
Given parameters are
𝜃=20∘.
N =1000 lines per mm length.
So, d =1𝑁
i.e. d = 11000 mm
i.e. d = 10−6 m.
For n =1,
using the formula, n 𝜆=𝑑𝑠𝑖𝑛(𝜃)
𝜆=𝑑𝑠𝑖𝑛(𝜃 putting n =1
= 10−6×𝑠𝑖𝑛20∘
= 3.4×10−5𝑚
Thus, the wavelength will be 3.4×10−5𝑚
More such examples are available for easy access on the Extramarks website and mobile application.
