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National Bird Day is celebrated every year on 5 January . This day is observed to spread awareness about birds, their importance in nature, and the need to protect them. Birds are beautiful living beings and play a very important role in keeping our environment healthy. Origin of National Bird Day National Bird Day was first celebrated in the year 2002 . It was started by bird lovers and environmental groups to protect birds from dangers like deforestation, pollution, and illegal hunting. The main aim of this day is to teach people, especially students, why birds are important and how we can help save them. Why Is National Bird Day Celebrated Every Year? National Bird Day is celebrated every year because many bird species are disappearing due to human activities. Cutting trees, using plastic, pollution, and climate change are harming birds and their homes. This day reminds us that: Birds need protection Nature should be respected Everyone has a responsibil...
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Coaxial lens system and its cardinal points | Optics | General theory of image formation

Coaxial lens system and its cardinal points

  • Let two lenses of focal lengths f1 and f2 are placed at a distance d from each other as shown in figure.

Coaxial lens system
  • If δ1 and δ2 are the deviations produced by lens L1 and L2, then
  • Total deviation produced by lens system
                    δ = δ1 + δ2                                                                            ...(1)

Equivalent focal length 

  • The deviation produced by a thin lens, δ = h / f
            ∴     δ1 = h1 / f1,    δ2 = h2 / f2    and    δ = h1 / F    ...(2)
  • Here F is the equivalent focal length of the lens system.
  • From equations (1) and (2), we get
                     
  • From figure
            O2C = O2P - CP                (∵  δ1 = CP / BP)
            
            h2 = h1 - (BP) δ1

            h2 = h1 - d (h1 / f1) = h1 (1 - d / f1) 

            

  • Here Δ is known as optical separation.
  • If P1 and P2 are the power of L1 and L2, and P is the power of lens system
            P = P1 + P2 - d P1P2

Position of second focal point (O2F2 = β2)

  • The real points from where the distances can be measured are O1 and O2
  • The distance of F2 will be measured from O2,
            O2F2 = β2
  • From ΔM2H2F2 and ΔCO2F2

Position of second principal point (O2H2 = α2)

  • The distance of second principal point is measured from the second optical centre O2
  • From figure, 
            H2O2 = H2F2 - O2F2
            α2 = F - β2             (∵  H2F2 = F and O2F2 = β2)

  • Since H2 lies to the left of L2
            

Position of first principal point (O1H1 = α1)

  • The distance of first principal point is measured from the first optical centre O1
                

Position of first focal point (O1F1 = β1)

  • The distance of first focal point can be measured from the first optical centre O1
  • From figure
                O1F1 = H1F1 - O1H1             (∵    H1F1 = F and O1H1 = α1)

                β1 = F - α1 

                
  • Since F1 lies to the left of L1
             
To know more about cardinal points of a lens system please click on the link https://youtu.be/_15xR0-N7ho or https://youtu.be/rq4Yoq9JiQc
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