A container contains water upto a height of 20 cm and there is a point source at the centre of the bottom of the container. A rubber ring of radius r floats centrally on the water. The ceiling of the room is 2.0 m above the water surface. (a) Find the radius of the shadow of the ring formed on the ceiling if r = 15 cm. (b) Find the maximum value 'of r for which the shadow of the ring is formed on the ceiling. Refractive index of water= 4/3.
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Answer:
(a) r=15 cm
∵ d=
(
n
air
n
center
)
d
⇒ d=
4
3d
⇒ FC=
4
3
AC=
4
3
×20=15 cm
Now, ∵ FC=BC ⇒∠BFC=450
o
⇒ EF=ED
⇒ ED=200+15
⇒ EG=215 cm
So radius of shadow =215 cm
(b) we know that at the maximum values of the light ray will undergo total internal reflection.
From figure:-
sinC=
n
water
I
=
4
3
Area from ΔABD
sinC=
BD
2
+AD
2
BD
⇒
4
3
=
BD
2
+(20)
2
BD
⇒ 9 BD
2
+3600=16 BD
2
⇒ 7 BD
2
=3600
⇒ BD
2
=514.28
⇒ BD=
514.28
=22.68 cm
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