1oh i see then the above method should work
this was toughest question in inpho2008
others were too easy
try part b
Sunlight falls on the convex surface of the plano - convex lens of aperture 0.080 m. The
radius of curvature of the convex surface of the lens is 0.100 m. The refractive indices of
the material of the lens for extreme red and violet colours of sunlight are 1.600 and 1.700
respectively.
(a) Calculate the positions of the observed image of the Sun with violet and red center.
(b) Calculate the sizes of the observed image of the sun with violet and red center.
[ 3 + 7 = 10 ]
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17 Answers
9yes u should apply geometry
thats what i told in my previous post
but your method of appromating lens to prism isnt valid
just apply lens formula twice after changing v after first refraction by 7cm
u get focus and then find inercept eq and diffrentiate to get maxima
1but if i apply geometry there shoudnt be any problem(as i did by the second method i posted)!
it is always valid!
9good point
well our eye has focus of 2.5 cm and screen is also small
then also when we look at sun the whole retinal screen is illuminated with sunlight
with focus having maximum intensity
in the question your method is applicable for finding first intensity central illuminance but when whole lens is subjected to rays there is a region of illuminance when u consider refraction. there are areas where light cant reach under parrellel incidence for any point .
try to obtain a general formula for intercept of emergent ray at focal plane
differentiate it to get maxima and it gives u region of illuminance
1i mean to say that our eye also acts as a lens
but the size of the sun and the size of other stars are not the same!!
1i dont think that is needed
as i have posted my second method without using any formula just the snell's law which is valid every where
moreover if you say that the radius of the sun and the distance wont come into picture do you mean to say the even it would have been the moon the image size would be same?
9moreover Radius and Distance of sun dont come into picture when solving
take all rays to be parrallel and falling normally on lens
find maximum height of illuminance at focus
1i dont think part b is tough
see the figure
the image of the vertical diameter of the sun will be formed at the focus(as we take distance of sun to be at infinity)
let the radius of the image be t
the image of the diameter will be as shown (as all the points are at the same distance)
and from the eqn
1/f=(n21-1)(1/R1-1/R2)
for violet light
1/fv=(1.7-1)(1/.1-1infinity)=(.7)(10)=7m
and for red light
1/fr=6m
hence the image of the vertical diameter will be formed at 7m in the other side
and further the image of the topmost point in the diameter will be formed
along the line which passes through the pole
hence from figure ,√ACB=√DCE
so tan√ACB=tan√DCE
so R/D=t/f
t=f*R/D
placing the value of R as 7* 108
and D as 1.5*1011
and the earlier obtained value of f as 7m
we get t= 3.26 *10-2 for violet light and
t=2.8*10-2 for red light
1by the way this problem can be solved by another method too
instead of applying the lens maker's formula we can take two rays one passing through the pole(which will
go straight) and another passing through the upper extremity of the lens (considering it as a prism and applying snell's law)
we will get it as a right angled prism with one angle = sin inverse (A/2R)
A = aperture R=radius of curvature
the point where they will meet can be found out ;
then the distance of the point from the principal axis will be the radius (were u talking of this method?)
1as it is plano convex i hv taken radius of first part = .1m
and of second part infinity whats wrong?
9no ur formula is also wrong
its an olympiad question for 7marks
solution quite long and interesting!!!!
1by mistake the figur may be wrong but i hv calculated everything considering it as a plano convex lens
9rohan see the question again
its for a plano convex lens
solution not as easy as it seems