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महाराणा प्रताप ट्रेल सज्जनगढ़ उदयपुर

महाराणा प्रताप ट्रेल सज्जनगढ़ उदयपुर में इको ट्रेल 30 नवम्बर को राजस्थान वन विभाग उदयपुर डिविजन तथा WWF-India उदयपुर डिविजन के सानिध्य में महाराणा प्रताप ट्रेल सज्जनगढ़ उदयपुर में इको ट्रेल की गई, जिसमें WWF-India के स्टेट काॅर्डिनेटर श्रीमान अरूण सोनी तथा वन विभाग कीे ओर से डाॅ. सतीश कुमार शर्मा, सेवानिवृत्त अधिकारी मौजूद थे। मुझे भी इस इको ट्रेल में जाने का सुअवसर प्राप्त हुआ, जो गोरीला व्यू पाॅइंट से बड़ी-लेक व्यू पाॅइंट तक की गई इसमें मुझे विज्ञान की एक नई शाखा के बारे में पता चला, जिसे टट्टी विज्ञान कहा जाता है। सुनने में आपको थोड़ा अजीब लगेगा, मुझे भी सुनकर हैरानी हुई, परन्तु वास्तव में एक ऐसा भी विज्ञान है, जिसके बारे में डाॅ. सतीश शर्मा ने बड़े ही विस्तार पूर्वक बताया कि किस प्रकार वनों में जानवरों की टट्टी देखकर यह पता लगाया जा सकता है कि यहां कौनसा जानवर आया था। जानवरों की टट्टी कितनी पुरानी है, वह गीली है या सूखी है। इसी के आधार पर उस विशेष जंगल में कौन-कौनसे जानवर विचरण करते हैं, उसके बारे में वन विज्ञान के कर्मचारी पता लगा लेते हैं। जानवरों की टट्टी का विश्लेषण करके यह पता लगा...
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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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