(i) Consider a thin lens placed between a source (S) and an observer (O) (Figure). Let the thickness of the lens vary as w(b) =w0– b2/α , where b is the vertical distance from the pole, w0is a constant. Using Fermat’s principle, i.e., the time of transit fora ray between the source and observer is an extremum find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.
(i) Consider a thin lens placed between a source (S) and an observer (O) (Figure). Let the thickness of the lens vary as w(b) =w0– b2/α , where b is the vertical distance from the pole, w0is a constant. Using Fermat’s principle, i.e., the time of transit fora ray between the source and observer is an extremum find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.
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1 Answer
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This is a long answer type question as classified in NCERT Exemplar
Time from S to P1 is
t1 =
Time from P1 to O is
t2 = ;
the time required travel through lens is t1 =
so total time is t=1/c(u+v+b2/2D+(n-1)(wo+b2/ ))
after solving we get
differentiating with respect to time
t=1/c(u+v+b2/2D+(n-1)K1In(K2b))
dt/db=0=b/D-(n-1)K1/b
b2= (n-1)K1D
b=
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