Angular Distribution of Diffraction Orders in Diffraction Grating

When monochromatic light falls on a diffraction grating diffraction patterns are produced on the other side of the grating. The angular distribution of the diffraction orders are given by

( a + b ) * sin(theta) = n*lambda

or, theta = asin(n*lambda / ( a + b ) )

where,
'( a + b )' is called grating element,

'theta' is angle of diffraction,
'n' is the order of diffraction
and 'lambda' is the wavelength of light used.

To demonstrate the variation of diffraction angle with orders, a program written using OCTAVE is  presented below.
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clear all
close all

ge = 2.54/15000; % ge(grating element) = (a + b)
lambda = 5893e-8; % wavelength of sodium light
n = [1 2 3];

theta = asind(n*lambda/ge);

plot(n,theta,'mh','MarkerSize',20)
xlabel('n'), ylabel('theta'),title('Angular Distribution of Diffraction Orders in Diffraction Grating')
grid on
axis([0 4 0 95])
print('fig(1).jpg')


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The result of above program is shown on the figure.

Glimpses of Hiking to Lakuri Bhanjyang.

240 degree panoramic view from Lakuri Bhanjyang.

Tea at Lamatar-5, Dhungin, Lalitpur
(1 and half hours from Kirtipur using Public vehicles, trek  starts here)

View of the city from the way towards Lakuri.

Simple map of the trekking route hanged on a home at Lakuri peak
 (almost 2 hrs from Dhungin, on foot).

At Khaja ghar with "Dal", "Bhat", "Tarkari".

On the way from Lakuri to Panauti.

On the way from Lakuri to Panauti.

On the way from Lakuri to Panauti.

Boarder of Lalitpur and Kavrepalanchok District.

On the way from Lakuri to Panauti.

On the way from Lakuri to Panauti.

Panauti Bus Park (almost 4 hrs from Lakuri, on foot)

"Pi" and popular misconception.

The number π is a mathematical constant that is the ratio of a circle's circumference to its diameter. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes romanticized as "pi".

  

Being an irrational number, π cannot be expressed exactly as a ratio of any two integers (fractions such as 22/7 are commonly used to approximate π but no fraction can be its exact value).In fact, pi has been calculated to over two quadrillion decimal places and still there is no pattern. 

The value of pi to 100 significant figures is 

3.14159265358979323846264338327950288419716939937510582097 

4944592307816406286208998628034825342117067... 

The  value of pi up to 100,000 digits can be viewed on the site 

http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html

There is also a movie  featuring  the pattern of pi whose trailer can be viewed  below.