Refraction through a

spherical surface

 

1) Suppose O is an object



2) light coming from O passing through the pole P and centre of curvature C do not changes its path after refraction. As shown below.





3) Another rays coming from O incident at position M of the interface of the denser medium & After refraction the rays meets the principal rays at I position.




4) As two real rays coming from the object O meets at I, therefore I is the real image of O.



5) A normal is drawn from the centre of curvature C to the position M.


6) Another normal from M to the principal axis is draw ML is also drawn.   



7) Now i is the incident angle and r is the refractive angle.



8) Now x, y, & z are the angles <MOL, <MCL, & <MIP




Respectively. For small values of x, y, & z









9) Now from 


i = x + y



& from  


y = r + z

r = y - z

 




10) Now from Snell’s Law

 


 





 

For small values of x, y, & z


OL = OP = -u

LC = PC = +R

LI = PI = +v



11) Putting the value of these on 9.23