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Bhupal Nobles' University, Udaipur Convocation | भूपाल नोबल्स विश्वविद्यालय, उदयपुर दीक्षांत समारोह

भूपाल नोबल्स विश्वविद्यालय दीक्षांत समारोह महाराणा प्रताप स्टेशन रोड, सेवाश्रम सर्कल, उदयपुर। भूपाल नोबल्स विश्वविद्यालय उदयपुर द्वारा वर्ष 2018 से 2024 तक की स्नातक एवं स्नातकोत्तर परीक्षा में उत्तीर्ण एवं विद्यावाचस्पति (Ph.D.) उपाधिधारियों के लिए दीक्षान्त समारोह 27 मार्च 2025 गुरूवार को प्रातः 10:30 बजे आयोजित करने का निश्चित हुआ है। दीक्षान्त समारोह में 2020 से 2025 तक की विद्यावाचस्पति की उपाधियों तथा स्नातक एवं स्नातकोत्तर परीक्षाओं में वर्ष 2024 तक प्रथम स्थान प्राप्त करने वाले छात्रों को उपाधि एवं स्वर्ण पदक प्रदान किए जायेंगे। अतः जो उपाधिधारी उक्त समारोह में उपाधि प्राप्त करने के इच्छुक हों, वे समारोह में उपस्थित होने की लिखित सूचना के साथ स्नातक एवं स्नातकोत्तर प्रथम वरीयता प्राप्त छात्रों हेतु, पंजीकरण शुल्क ₹500 व उपाधि शुल्क ₹5000 (कुल ₹5500) एवं विद्यावाचस्पति (Ph.D.), शोधार्थी पंजीकरण शुल्क ₹500 व उपाधि शुल्क ₹5000 (कुल ₹5500) नकद अथवा डिमाण्ड ड्राफ्ट भूपाल नोबल्स विश्वविद्यालय, उदयपुर के नाम बनाकर कुलसचिव, भूपाल नोबल्स विश्वविद्यालय, उदयपुर को दिनांक 17.03.2025 तक ...
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Aplanatic points of a spherical refracting surface | Optics | General theory of image formation

Aplanatic points of a spherical refracting surface


  • From Abbe’s sine condition
                

            
  • If this ratio is constant for a particular surface, then the surface is known as aplanatic surface.
  • An aplanatic surface is a surface which forms a point image of a point object situated on its axis.
  • The image formed by aplanatic surface is free from optical aberrations.
  • Using sine law in △OPC
                    
            
                            ...(1)
  • Since refraction is taking place from denser to rarer, so from Snell's law
            
            
                            ...(2)
  • Now from above two equations, we get
            sin θ1 = sin r     ⇒     θ1 = r  
  • In ΔIOP,
            θ1 = θ2 + (r - i)     ⇒     θ2 = i
  • From ΔOCP and ΔICP
            
            
            
            
            
        
            
  • This relation does not depends on θ1 and θ2.
  • The beam divergent from O at any angle is definitely converged at I.
  • A point object O situated at a distance R/µ from C will be imaged on I at µR distance from C.
  • Since image is free from θ1 and θ2, so the image will be free from optical defects.
To know more about Aplanatic points of a spherical refracting surface click on https://youtu.be/IFrvMhwgQbQ
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