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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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Abbe’s sine condition | Optics

Abbe’s sine condition

Sign convention

For axial or longitudinal distance

  • The distances measured along optic axis or parallel to optic axis are known as axial or longitudinal distance.
  • All the distances measured in the direction of incident ray from optical centre O are taken as positive, and all the distances measured in the direction opposite to the incident ray are taken as negative.

For transverse or lateral distance

  • All the distances measured perpendicular to the optic axis are known as transverse or lateral distances.
  • The transverse distances above the optic axis are taken as positive and the transverse distances below the optic axis are taken as negative.

For angles

  • The angles measured in anticlockwise direction with optic axis are measured as positive, and the angles measured in clockwise directions are measured as negative.
  • ∠ θ1 is negative, and ∠θ2 is positive.

            Note

    • All the longitudinal distances should be measured from optical centre, and all the lateral distances should be measured from optic axis.


      Abbe’s sine condition

    • By using sign convention
    • h1 and v are positive.
    • h2 and u are negative
    • θ1 and i are positive, and θ2 is negative.
    • From △CNM and △CN՛M
    ՛
    • By using sine law in △ANC

    • By using sine law in △AN՛C
    • This is Abbe's since condition.
    • This relation is valid for all the values of θ1 and θ2.
    • In this way a point N on axis imaged as N՛ on the axis by refraction from the surface XY.
    • A surface which does so, is known as aplantic surface, and this surface is used in objectives of microscopes.
    • If aperture of the refracting surface is very small, then θ1 and θ2 will be very small.
    • ∴   sin θ1 ≈ tan θ1 and sin θ2 ≈ tan θ2
    • µ1h1 tan θ1 = µ2h2 tan θ2
    • This is Lagrange’s equation.
    • Also if the values of θ1 and θ2 are very small, then tan θ1 ≈ θ1 and tan θ2 ≈ θ2
    • µ1h1 θ1 = µ2h2 θ2
    • This is Helmholtz equation.
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