Curve fitting is the process of constructing a curve or mathematical function, that has the best fit to a series of data points. Fitted curves can be used as an aid for data visualization, to conclude values of a function where no data are available, and to summarize the relationships among two or more variables.
Equation for Cauchy Curve is, $$ Y=\frac { I }{ \left[ 1+{ \left( \frac { x-a }{ \gamma } \right) }^{ 2 } \right] } $$ Where \(I\) is intensity,
\(a\) is Position,
\(\gamma\) is Scale parameter
Equation for Cauchy Curve is, $$ Y=\frac { I }{ \left[ 1+{ \left( \frac { x-a }{ \gamma } \right) }^{ 2 } \right] } $$ Where \(I\) is intensity,
\(a\) is Position,
\(\gamma\) is Scale parameter
The Perfect Cauchy or Lorentzian Curve fitting in MS Excel
Curve fitting is the process of constructing a curve or mathematical function, that has the best fit to a series of data points. Fitted curves can be used as an aid for data visualization, to conclude values of a function where no data are available, and to summarize the relationships among two or more variables.
Equation for Cauchy Curve is, $$ Y=\frac { I }{ \left[ 1+{ \left( \frac { x-a }{ \gamma } \right) }^{ 2 } \right] } $$ Where \(I\) is intensity,
\(a\) is Position,
\(\gamma\) is Scale parameter
Equation for Cauchy Curve is, $$ Y=\frac { I }{ \left[ 1+{ \left( \frac { x-a }{ \gamma } \right) }^{ 2 } \right] } $$ Where \(I\) is intensity,
\(a\) is Position,
\(\gamma\) is Scale parameter
Curve fitting is the process of constructing a curve or mathematical function, that has the best fit to a series of data points. Fitted curves can be used as an aid for data visualization, to conclude values of a function where no data are available, and to summarize the relationships among two or more variables.
Equation for Gaussian Curve is, $$ Y = A.{ e }^{ -\left( \frac { { \left( x-B \right) }^{ 2 } }{ 2{ C }^{ 2 } } \right) } $$ Where \(A\) is Height,
\(B\) is Position and
\(C\) is FWHM.
Equation for Gaussian Curve is, $$ Y = A.{ e }^{ -\left( \frac { { \left( x-B \right) }^{ 2 } }{ 2{ C }^{ 2 } } \right) } $$ Where \(A\) is Height,
\(B\) is Position and
\(C\) is FWHM.
The Perfect Gaussian Curve fitting in MS Excel
Curve fitting is the process of constructing a curve or mathematical function, that has the best fit to a series of data points. Fitted curves can be used as an aid for data visualization, to conclude values of a function where no data are available, and to summarize the relationships among two or more variables.
Equation for Gaussian Curve is, $$ Y = A.{ e }^{ -\left( \frac { { \left( x-B \right) }^{ 2 } }{ 2{ C }^{ 2 } } \right) } $$ Where \(A\) is Height,
\(B\) is Position and
\(C\) is FWHM.
Equation for Gaussian Curve is, $$ Y = A.{ e }^{ -\left( \frac { { \left( x-B \right) }^{ 2 } }{ 2{ C }^{ 2 } } \right) } $$ Where \(A\) is Height,
\(B\) is Position and
\(C\) is FWHM.
Curve fitting is the process of constructing a curve or mathematical function, that has the best fit to a series of data points. Fitted curves can be used as an aid for data visualization, to conclude values of a function where no data are available, and to summarize the relationships among two or more variables.
Equation for Exponential Decay Curve is, $$ Y = \frac { 1 }{ B } .{ e }^{ \left( \frac { { A-x } }{ B } \right) } $$Where \(A\) is Position,
\(B\) is Scale parameter
Equation for Exponential Decay Curve is, $$ Y = \frac { 1 }{ B } .{ e }^{ \left( \frac { { A-x } }{ B } \right) } $$Where \(A\) is Position,
\(B\) is Scale parameter
The Perfect Exponential Curve fitting in MS Excel
Curve fitting is the process of constructing a curve or mathematical function, that has the best fit to a series of data points. Fitted curves can be used as an aid for data visualization, to conclude values of a function where no data are available, and to summarize the relationships among two or more variables.
Equation for Exponential Decay Curve is, $$ Y = \frac { 1 }{ B } .{ e }^{ \left( \frac { { A-x } }{ B } \right) } $$Where \(A\) is Position,
\(B\) is Scale parameter
Equation for Exponential Decay Curve is, $$ Y = \frac { 1 }{ B } .{ e }^{ \left( \frac { { A-x } }{ B } \right) } $$Where \(A\) is Position,
\(B\) is Scale parameter
Curve fitting is the process of constructing a curve or mathematical function, that has the best fit to a series of data points. Fitted curves can be used as an aid for data visualization, to conclude values of a function where no data are available, and to summarize the relationships among two or more variables. An equation for Straight Line is, Y = MX + C Where M is slope and C is intercept
The perfect line fitting in MS Excel
Curve fitting is the process of constructing a curve or mathematical function, that has the best fit to a series of data points. Fitted curves can be used as an aid for data visualization, to conclude values of a function where no data are available, and to summarize the relationships among two or more variables. An equation for Straight Line is, Y = MX + C Where M is slope and C is intercept
Plane Mirror
Image formed is as far behind the mirror as the object is in front of it, with the lateral inversion of image. i.e. right hand side of object is left hand side of image and vice versa.
Convex Mirror
Image formed is always virtual, erect and diminished.
Concave Mirror
Depending upon the position of the object, size of the image formed can be equal to, larger than or smaller than the size of object. Also the nature of image formed may be real or virtual.
How can you distinguish between a plane, convex and concave mirrors?
Plane Mirror
Image formed is as far behind the mirror as the object is in front of it, with the lateral inversion of image. i.e. right hand side of object is left hand side of image and vice versa.
Convex Mirror
Image formed is always virtual, erect and diminished.
Concave Mirror
Depending upon the position of the object, size of the image formed can be equal to, larger than or smaller than the size of object. Also the nature of image formed may be real or virtual.
The distance between the principal focus of a mirror and the pole of mirror is called focal length of the mirror.
In case of Concave mirror distance between the pole ‘O’ and principal focus ‘F’ of mirror is focal length and is always taken as negative.
In case of Convex mirror distance between the pole ‘O’ and principal focus ‘F’ of mirror is focal length and is always taken as positive.
The radius of Curvature of plane mirror is infinite, hence the focal length of plane mirror will also be infinite.
Define focal length. What is the focal length of plane mirror, concave mirror and convex mirror?
The distance between the principal focus of a mirror and the pole of mirror is called focal length of the mirror.
In case of Concave mirror distance between the pole ‘O’ and principal focus ‘F’ of mirror is focal length and is always taken as negative.
In case of Convex mirror distance between the pole ‘O’ and principal focus ‘F’ of mirror is focal length and is always taken as positive.
The radius of Curvature of plane mirror is infinite, hence the focal length of plane mirror will also be infinite.
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