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National Bird Day: Why Birds Matter to Us

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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Thick lens and its cardinal points | Optics | General theory of image formation

Thick lens and its cardinal points

Thick lens

  • The combination of two spherical surfaces, is known as thick lens, if the distance between their poles can not be neglected in comparison to their radii.
  • It can be treated as the combination of thin lenses.
  • The thickness of these lenses are comparable to their focal lengths.

Cardinal points of thick lens

  • Let µ = refractive index of material of lens
  • t = thickness of lens
  • R1 and R2 = Radii of curvature of first and second curved surface of the given thick lens.
  • F1 and F2 = First and second focal points respectively.
  • H1 and H2 = First and second principal points respectively.
  • f1 and f2 = First and second focal length of thick lens respectively.

Cardinal points of thick lens

Equivalent focal length

  • If there is same medium on either side of thick lens
  • H1F1 = f1 = - f , and H2F2 = f2 = f

Refraction from surface PP1


Refraction from surface QP2

  • This time I works as an object and forms final image is obtained at F2



  • For thin lens t → 0, and f → f0

Power of thick lens


Position of second focal point (P2F2 = β2)

  • The distance of second focal point will be measured from pole of second refracting surface.

Position of second principal point (P2H2 = α2)

 
  • The distance of second principal point will be measured from pole of second refracting surface

  • Above result is obtained using sign convention.

Position of first focal point (P2F1 = β1)

 
  • For obtaining it we consider that the ray is incident on lens system from right i.e., O՛Q, this time image will be formed on F1. So in β2, R1 is replaced by -R2 and f is replaced by -f.


Position of first principal point (P1H1 = α1)

 
  • For it we use R1 → –R2 and  f → – f in second principal point α2 

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