i) Time taken by the ray to travel from S to P1 is = t1 = √u2 + b2/c Time taken by the ray to travel from P1 to O is = t2 = v/c (1+ ½ b2/v2) Time taken to travel through the lens is =...
(i) Consider a thin lens placed between a source (S) and an observer (O). Let the thickness of the lens vary as 2 0 () – α = b wb w, where b is the verticle distance from the pole. w0 is a constant. Using Fermat’s principle i.e. the time of transit for a 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.
(ii) A gravitational lens may be assumed to have a varying width of the form w(b) = k1 ln (k2/b) = k1 ln (k2/bmin). Show that an observer will see an image of a point object as a ring about the centre of the lens with an angular radius.
β = √(n-1)k1 u/v / u + v
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. If 
= 
, it’s de Broglie wavelength at time t is given bya) 
b) 
c) 
d ) 
It’s de Broglie wavelength at time t is given bya) 
b) 
c) 
, where 
? Give reasons for your answer.
and 
. Their energy levels, as worked out on the basis of Bohr model will be very close. Explain why.
atom because
of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows: ![\[\begin{tabular}{|l|l|l|l|l|l|} \hline$t(\mathrm{~h})$ & 0 & 1 & 2 & 3 & 4 \\ \hline R(MBq) & 100 & $35.36$ & $12.51$ & $4.42$ & $1.56$ \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2cff4d33a1ea1a3274f405d5eee59de6_l3.png "Rendered by QuickLaTeX.com")
and calculate half-life from the graph.
versus 
and obtain the value of half-life from the graph.
and 
?
, where r is in km and
melectron 
magnitude of the potential energy of electron in the 
-atom)
over the rectangular loop 1234 shown in the figure
over the surface bounded by loop 1234
is placed symmetrically along the z-axis and has radius 
. The cable consists of a thin wire and a co-axial conducting tube. An alternating current 
sin 
flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance 
from the wire inside the cable is 
. In 
, 
is used in satellite communication
is used to kill germs in water purifies
is used to detect leakage of oil in underground pipelines
is used to improve visibility in runaways during fog and mist conditions
. What is the average intensity of the beam?
nm (c) 
nm (d)
nm
Choose the correct options from the following:
as the amplitude of its electric field vector. The electric field 
which transports significant energy from the source falls off as
and 
represent electric and magnetic field vectors of the electromagnetic wave, the direction of propagation of the electromagnetic wave is along
bulb at a 
distance is E. The electric field intensity produced by the radiations coming from 
bulb at the same distance is
falls on a non-reflecting surface at normal incidence. If the surface has an area of 
, the total momentum delivered during 30 minutes is
is incident normally on a perfectly reflecting infinite wall at 
.
a) show that
monotonically increases with L b) use an appropriate Amperian loop to that
where I is the current in the wire c) verify directly the above result d) suppose we replace the circular coil by a square coil of sides R carrying the same current I. What can you say about
b) the value of
c) there may be a point on C where B and dl are perpendicular d) B vanishes everywhere on C