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भारतीय रसायन के पिता आचार्य प्रफुल्ल चंद्र रे की जयंती पर व्याख्यान का आयोजन

भारतीय रसायन के पिता आचार्य प्रफुल्ल चंद्र रे की जयंती पर व्याख्यान का आयोजन विज्ञान भारती उदयपुर इकाई एवं बीएन कॉलेज ऑफ फार्मेसी, बीएन विश्वविद्यालय के संयुक्त तत्वावधान में कार्यक्रम सम्पन्न उदयपुर, 2 अगस्त। भारतीय रसायन के पिता आचार्य प्रफुल्ल चंद्र रे की जयंती के अवसर पर विज्ञान भारती उदयपुर इकाई (चित्तौड़ प्रांत) एवं बीएन कॉलेज ऑफ फार्मेसी, बीएन विश्वविद्यालय के संयुक्त तत्वावधान में एक विशेष व्याख्यान का आयोजन किया गया। कार्यक्रम का उद्देश्य आचार्य पी.सी. रे के वैज्ञानिक योगदान एवं उनके देशभक्ति से ओतप्रोत जीवन पर प्रकाश डालना था। ज्ञातव्य है कि भारत की पहली फार्मा कंपनी आचार्य रे ने ही बंगाल केमिकल एंड फार्मास्यूटिकल्स लिमिटेड, कोलकाता में 1901 में प्रारंभ की थी। कार्यक्रम में विज्ञान भारती के उद्देश्य एवं गतिविधियों की जानकारी डॉ. अमित गुप्ता द्वारा दी गई। आचार्य पी.सी. रे के जीवन और कार्यों पर मुख्य व्याख्यान डॉ. लोकेश अग्रवाल द्वारा प्रस्तुत किया गया। उन्होंने बताया कि कैसे आचार्य रे ने विज्ञान को समाज की सेवा का माध्यम बनाया और रसायन विज्ञान में भारत को आत्मनिर्भर बनान...
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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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