1. Xtra Edge February 2012 - Career Point

28 Parallel light rays incidenting over a lens converges
to a point (convex lens) or seems to diverge from the
point (concave lens) after refraction from lens. Then
this point is called principle focus of lens.
When lens is dipped into a liquid of refractive index
greater than lens material refractive index then
nature of lens gets changed.
Focal length of lens is maximum for red and
minimum for violet colour.
I
– µ1 = 1
µ1 = 1 +
µ2
II
R1 = + 20; R2 → ∞ ;
1 ⎛ 1 1 ⎞
= (µ2 – 1) ⎜ − ⎟
f
⎝ + 20 ∞ ⎠
1 ⎛ ⎞
= (2 –1) ⎜ − ⎟⎠
f ⎝ ∞
1 1
20
∴ f = + 20cm
OR
O
µ1
α
i
u P
M
R
By snell's law
m1 sin i = µ2 sin r
r
β γ
v
C
µ2
But for small aperture MP;
µ1i = µ2r …(i)
In ∆OCM; i = α + β
and In ∆ICM; β = r + γ ⇒ r = β – γ.
∴ By (i)
µ1 (α + β) = µ2 (β – γ)
⎡ MP MP ⎤ ⎡ MP MP ⎤
µ1 ⎢ + ⎥ = µ2
⎣ OP PC
⎢ − ⎥
⎦ ⎣ PC PI ⎦
⎡ 1 1 ⎤ ⎡ 1 1 ⎤
µ1 ⎢ + ⎥ = µ2
⎣−
u + R
⎢ − ⎥
⎦ ⎣ + R + v ⎦
–
µ 1 µ 1 µ 2 µ 2
+ = −
u R R v
µ 2 µ 1 µ 2 − µ 1
− =
v u R
I
29. Principal of van deGraff Generator : (i) Let a
small charged conducting shell of radius
r be located inside a larger charged conducting shell
of radius R. If they are connected with a conductor,
then charge q from the small shell will move to the
outer surface of bigger shell irrespection of its own
charge Q.
Here potential difference
XtraEdge for IIT-JEE 76 FEBRUARY 2012
R
r
q
= V(r) – V(R)
q
=
4πε
0
⎟ ⎛ 1 1 ⎞
⎜ –
⎝ r R ⎠
In this way, the potential of the outer shell increases
considerably.
(ii) Sharp pointed surfaces have larger charge
densities, so these can be used to set up discharging
action.
Conducting
S
Shell
Grounded
Steal
Tank
C1 , C2
metal
Comb
H
vR
C2
Q
Target
Insulating
Column
Working :Let spray comb C1 be charged to a high +ve
potential which spray +ve charge to the belt which in
turn becomes positively charged. Since belt is
moving up, so it carries this positive charge upward.
Opposite charge appears on the teeth of collecting
comb C2 by induction from the belt. As a result of
this, positive charge appears on the outer surface of
shell S. As the belt is
moving continuously, so the charge on the shell S
increase continuously. Consequently, the potential
of the shell (S) rises, to a very high value.
Now the charged particles at the top of the tub (T)
are very high potential with respect to the lower end
of the tube which is earthed. Thus these particles get
accelerated downward and hit the target emerging
from the tube.