Content Curator
A diffraction grating can be expressed as an optical component with a periodic structure that splits light into multiple beams traveling in different directions. Making several parallel scratches on the surface of a flat piece of transparent material results in a diffraction grating.
- When light strikes a diffraction grating, it multiplies for the source with parallel slits.
- An example includes when a flat piece of transparent material is scratched with numerous parallel lines to create a diffraction grating.
- The material is susceptible to several scratches per centimeter.
- For instance, the grating used will have 6,000 lines per cm.
- Although the scratches are opaque, the gaps between them let light through.
- Light creates a multiplicity for the source with a parallel slit when it hits a diffraction grating.
Read Also: Resolving Power of Microscopes and Telescopes
| Table of Content |
Key Terms: Diffraction, Diffraction Grating, Spectra, Light, Prism, Interference, Wavelength, Slits
What is Diffraction Grating?
[Click Here for Sample Questions]
A periodic optical element called a diffraction grating divides light into several beams that go in various directions. It serves as an alternative method for studying spectra to prisms.
- The divided light will frequently have maxima at an angle when light reaches the grating.
- On the grating, the rays will land in a parallel bundle.
- Since the rays and wavefront are an orthogonal set, the wavefront will be perpendicular to the rays and parallel to the grating.
- In this situation, Huygens' Principle is applicable.
- It states that every point on a wavefront and each transparent slit operate as new sources, causing cylindrical wavefronts to expand out from each.
- The waves cancel if a peak hits a valley repeatedly, therefore there is no light there.
- Additionally, the light appears stronger where valleys frequently fall into peaks and peaks fall into valleys.
- An alternative to using a prism to find spectra is diffraction.
Read Also:
Diffraction Grating Formula
[Click Here for Previous Year Questions]
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,
Then, the Diffraction Grating Formula can be expressed as,
nλ = d sinθn
Where,
- n = order of grating (n = 1, 2, 3)
- d = distance between two fringes or spectra
- λ = wavelength of light
- θ = angle to maxima
Note: A grating element is also the distance between two successive slits (lines) of the grating. Calculated for grating element "d". Thus, the Grating element, d = Grating length/Line count.
Read Also: Brewster's Law Formula
Solved Examples
Ques. Light is diffracted at 20o by a diffraction grating. If there are 2000 lines per millimeter of grating length, what will the wavelength of the light be?
Ans. Given the conditions are,
- θ = 20o.
- N = 2000 lines per millimeter
⇒ Thus, d =1/N
⇒ d = 1/2000 mm
⇒ d = 0.5 x 10−6 m.
For n =1,
Using the formula λn = dSinθn, (by setting n to 1)
λ = 0.5 x 10− 6 × sin 20o
λ = 0.17 × 10− 6 m = 1.7 x 10-7 m
Therefore, the wavelength will be 1.7 x 10-7 m.
Ques. Light is diffracted at 30o by a diffraction grating. If there are 1000 lines per millimeter of grating length, what will the wavelength of the light be?
Ans. Given the conditions are,
- θ = 30o.
- N = 1000 lines per millimeter
⇒ Thus, d =1/N
⇒ d = 1/1000 mm
⇒ d = 10−6 m.
For n =1,
Using the formula λn = dSinθn, (by setting n to 1)
λ = 10− 6 × sin 30o
λ = 10− 6 x 0.5 m
Therefore, the wavelength will be 0.5 x 10-6 m.
Previous Year Questions
- In an interference experiment, the ratio of amplitudes of coherent waves is…? [JEE Mains 2019]
- Diameter of the objective lens of a telescope is 250cm. For light of wavelength 600nm…? [JEE Mains 2019]
- Unpolarized light of intensity I is incident on a system of two polarizers, A followed by B…? [JEE Mains 2018]
- Light of wavelength 550 nm falls normally on a slit of width 22.0×10−5cm…? [JEE Mains 2018]
- An observer is moving with half the speed of light towards a stationary …? [JEE Mains 2017]
- A plane polarized light is incident on a polariser with its pass axis …? [JEE Mains 2018]
- Two light sources are said to be coherent if they are obtained from … [VITEEE 2010]
- The Brewster's angle … [NEET 2020]
- A linear aperture whose width is … [NEET 2016]
- At the first minimum adjacent to the central maximum of … [NEET 2015]
- In a diffraction pattern due to a … [NEET 2016]
- In a Young' double slit experiment … [NEET 2019]
Things to Remember
- When a diffraction grating is lit by a wide-spectrum (for instance, continuous light source), the colors of "rainbow" can be produced.
- A diffraction grating is a periodic optical element used in optics that divides light into many beams that go in various directions (i.e., different diffraction angles).
- 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.
- When light strikes a diffraction grating, it multiplies for the source with a parallel slit.
Also Read:
| Chapter Related Topics | ||
|---|---|---|
| Polariser & Application | Destructive Interference | Coherent sources |
| Brewster’s Law | Interference of waves | Coherent and Incoherent Addition of Waves |
Sample Questions
Ques. What is Diffraction Grating? (1 mark)
Ans. Diffraction grating can be expressed as a periodic optical element that divides light into several beams that go in various directions.
Ques.Light is diffracted at 20 by a diffraction grating. If there are 1000 lines per millimeter of grating length, what will the wavelength of the light be? (3 marks)
Ans: Given conditions are,
Θ = 20∘.
1000 lines per millimeter
⇒ Thus, d =1/N
⇒ d = 1/1000 mm
⇒ d = 10−6 m.
for n =1,
Using the formula λn = dSinθn, (by setting n to 1)
= 10− 6 × sin20o
= 3.4 × 10− 5 m
Therefore, the wavelength will be 3.4 x 105 m.
Ques.Find the slit spacing for a diffraction grating with a 2 cm width that exhibits a 30° second-order deviation when illuminated by light with a 500 nm wavelength. (3 marks)
Ans: As per the question,
n = 2 is the order.
The deviation's angle, = 30°, and
The wavelength is 500 nm or 500 10-9 meters.
Using the diffraction grating formula, this follows:
nλ = d sin θ
2 × 500 × 10-9 m = d × sin 30°
d = 2 × 10-6 m
Ques. Monochromatic light illuminates a grating with 5000 slits per centimeter, which creates the second-order brilliant line at a 30° angle. Identify the light's used wavelength. (1 Å = 10-10 m) (3 marks)
Ans: n = 2 is the order.
The deviation's angle, = 30°, and
N = 5000, number of slits per cm
This indicates that d = 1/N = 1/5000 cm = 5 10-4 cm = 5 10-6 m is the distance between slits.
Using the diffraction grating formula, this follows:
nλ = d sin θ
2 × λ = 5 × 10-6 m × sin 30°
λ = 1.25 × 10-6 m
= 1250 Å
Ques. What is the slit spacing for a 1 cm wide diffraction grating that, when used with the light of 1000 nm wavelength, exhibits a 30-degree deviation in the fourth order? (3 marks)
Ans: The n-th order is 4.
The deviation's angle, = 30°, and
Its wavelength is 1000 nm or 1000 10-9 meters.
Using the diffraction grating formula, this follows:
nλ = d sin θ
4 × 1000 × 10-9 m = d × sin 30°
d = 8 × 10-6 m
Ques. Find the separation between the slits in a diffraction grating with a width of 1 cm that exhibits a 30° deviation in the second order when illuminated by light with a wavelength of 300 nm. (5 marks)
Ans: Here,
n = 2 is the order.
The deviation's angle, = 30°, and
The wavelength is 300 nm or 300 10-9 meters.
Using the diffraction grating formula, this follows:
nλ = d sin θ
2 × 300 × 10-9 m = d × sin 30°
d = 1.2 × 10-5 m
Ques. To produce a fourth-order brilliant line when monochromatic light with a wavelength of 600 nm strikes a grating at an angle of 30°, determine the number of slits per centimeter. (5 marks)
Ans. Here,
The n-th order is 4.
The deviation's angle, = 30°, and
The wavelength is 600 nm, which equals 600 10-9 m.
Using the diffraction grating formula, this follows:
nλ = d sin θ
4 × 600 × 10-9 m = d × sin 30°
or
d= 4.8 × 10-6 m
The number of slits per centimeter is now stated as follows:
x = 1 / 4.8 × 10-6 m
= 2.08 × 105/ m
= 2.08 × 105 / 102 cm
= 2.08 × 103 / cm
= 2080 / cm
Do Check Out:
Comments