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Single Slit Vs Multiple Slit Applications With Grating (Resolution) Numericals

In a multiple slit diffraction experiment, the resolution is proportional to the wavelength such that a lower wavelength provides higher resolution. An electron wave with a wavelength of 2 nm would provide better resolution than a visible light wavelength of 450 nm. The maximum number of lines per meter for a diffraction grating used with visible light, which has wavelengths from 400-700 nm, is 25,000 lines per meter. In a double slit experiment using light of different colors, the fringe widths will be in increasing order of blue, green, then red due to their increasing wavelengths over the visible spectrum.

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Somala Ashuthosh Reddy 19BEC1081
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85 views11 pages

Single Slit Vs Multiple Slit Applications With Grating (Resolution) Numericals

In a multiple slit diffraction experiment, the resolution is proportional to the wavelength such that a lower wavelength provides higher resolution. An electron wave with a wavelength of 2 nm would provide better resolution than a visible light wavelength of 450 nm. The maximum number of lines per meter for a diffraction grating used with visible light, which has wavelengths from 400-700 nm, is 25,000 lines per meter. In a double slit experiment using light of different colors, the fringe widths will be in increasing order of blue, green, then red due to their increasing wavelengths over the visible spectrum.

Uploaded by

Somala Ashuthosh Reddy 19BEC1081
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Single slit vs multiple slit

Applications with grating (resolution )


Numericals

m = asin n = dsin
(condition for min) (condition for max)
Resolution: is the shortest/minimum distance between two In a material characterization lab, they are two wave
points or objects that can be distinguished by the observer or sources. One is electron wave with wavelength of 2 nm
camera system and another one is electromagnetic wave with
wavelength of 450 nm. Which one would you prefer for
obtaining high resolution? Justify your answer.
Click to add text
What is the maximum number of lines per metre a

diffraction grating can have and produce a spectrum for


visible light?
Resolving power is proportional to wavelength
So to obtain higher resolution wavelength should be minimum
Ans: Electron wave with 2 nm
From diffraction condition What is the angular separation of two spectral lines of
wavelengths 550 nm and 600 nm formed on a screen with
n = dsin diffraction order n = 3 using a 529000 lines/m grating?
Since wavelength range
d = n /sin for visible light 400 nm 700 nm

Number of lines per metre = 1/d = sin /n


For maximum number lines sin = 1, n = 1 and = 400 nm
= 400 x 10-9 m
Maximum number lines = 1/(1x400 x 10-9) = 25x105 lines per
metre
A grating containing 4000 slits per centimetre is
n = dsin dsin = n = sin-1 (n /d)
illuminated with a monochromatic light and produces the
For 550 nm For 600 nm seconder order bright line at a 30°angle. What is the
wavelength of the light used?
1 = sin-1(n /d) 2 = sin-1(n /d)

1 = sin-1(3x550x10-9x529000) 2 = sin-1(3x600x10-9x529000)

1 = 60.28o 2 = 71. 33o

Angular separation = 1- 2 = 11.05o


Order of diffraction (n) = 2
From diffraction condition
Angle of diffraction ( ) = 30o
n = dsin
The distance between slits (d) = 1/no of slits per unit length
= dsin /n
= 1 / (4000 slits / cm)
= (2.5x10-6x0.5)/2
= 0.00025 cm
= 625x10-9 m
= 2.5 x 10-4 cm
= 625 nm
= 2.5 x 10-6 meters
Wavelength ( ) = ?
A double slit apparatus is immersed in a liquid of
refractive index 1.25. What is the ratio of the fringe width in air
and liquid? a = aD/d

l = lD/d

a l = a: l

a l a/ l = Va/Vl

a l = 1.25

a l =5:4
In Young's double slit experiment lights of Blue, green, and red
colors are successively used. Write the fringe widths for the Since = D/d
three color in increasing order. b = bD/d g = gD/d r = rD/d

Here b(450 nm) < g(550nm) < r(620nm)

Since is proportional to
Therefore b < g < r
Suppose you pass light from a He-Ne laser through two slits Given values:
separated by 0.01 mm and find that the third bright line on a
screen is formed at an angle of 10.95o relative to the incident d = 0.01 mm = 0.01 x 10-3 m
beam. What is the wavelength of the light? n = 3 and = 10.95o
Since path difference = n
dsin = n
= dsin /n
= (0.01 x 10-3 x sin10.95)/3
= 633 nm
Find the largest wavelength of light falling on double slits dsin = n
separated by 1200 nm for which there is a first-order
maximum. Is this in the visible part of the spectrum? n = dsin
= dsin /n = dsin
For largest wavelength sin = 1
Therefore largest =d

largest = 1200 nm
It is not in visible region since wavelength range of visible
region is 400 nm 700 nm
A thin sheet of refractive index 1.5 and thickness 0.01 m is
placed in the path of light from one source in the As we know, the path difference
double slit experiment. What is the path difference observed?
introduced by the sheet = 1) t,
where t is the thickness of the sheet.
Here, = 1.5 and t = 0.01 m
Therefore, = 0.25 X 0.005 m
=0.0012m = 1.25 mm.

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