ray optics, part 2 (physics) for jee main
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Ray OpticsBy :- prof. Dnyanesh Vaidya
What is Ray Optics The branch of physics that deals with
light and vision,
What is a lens? Lens is a peace of transparent medium
bounded by two curved surfaces or one curve and one plane surface.
Basic concept about lens
1. Optical centre : rays passes undeviated
2. Centre of curvature & Radius of
curvature :
Principal focus , Principal plane , Focal plane, Focal length :
New Cartesian sign conventions
Real Image formed by a single spherical surface
21 2
1
1 2
2
1
2 1
2 1
(1)
According to Snell’s law
sin(2)
sin1 2
sin
sin
sinr sin i
sin r r and sin i i
r i .. 3
i
rFrom and
i
r
For very small angles
2 1
2 2 1 1
2 1 1 2
2 1 1 2
From ODC i (4)
and from DIC r
r (5)
.4&5 3
( ) ( )
( ) 6
As , and are very small angles and expressed in ra
Sub in
dian
then form the diagram.
arcPD arcPD arcPD
PO Pl PC
2 1 1 2
2 1 1 2
2 1 1 2
1 2 2 1
2 1
Substituting these values in equation 6 , we get
( )
( )
The factor is called as power of surface.
arcPD arcPD arcPD
PC PO PI
PC PO PI
R u v
u v R
R
Lens maker’s equation
1
'
1
1 1
u v R
m - m- =
1 2 2 1
1 2
'1
'2
1 2
1
1, '
1 1(1)
2
1 1(2)
Adding equation 1 and 2 we can write
1 1 1 1( 1)
for surface
u v R
Let and v v
u v R
For surface
v v R
v u R R
1 2
1 2
1 2
1 2
When u and v f .
1 1 1( 1)
For concave lens R is negative and R is positive therefore,
1 1 1( 1)
1 1 1( 1)
f R R
f R R
f R R
Conjugate foci
Multiple Choice Questions
1. A plano convex lens is made of refractive index 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is (a) 50 cm (b) 100 cm(c) 200 cm (d) 400 cm
Ans: (b) 100 cm
1 2
1 1 11
f R R
1 1 0.6 11.6 1
60 60 100
f 100 cm
2. A convex lens has a focal length f. It is cut into two parts along a line perpendicular to principal axis. The focal length of each part will be(a) f/2 (b) f
(c) (d) 2f 3f
2
Ans: (d) 2f
1 1 1 21 1 ..... i
f R R R
11 1 11 ..... ii
f ' R R
Divide i by ii
f '2 f ' 2f.
f
Magnification “Ratio of linear size of image to linear
size of object is called as linear magnification.”
Power of lens
“The ability of a lens to converge or diverge the rays passing through it is called as power of lens.”
“Power of lens can also be defined as reciprocal of focal length in meter.”
Distance of Distinct Vision (DDV)
The minimum distance of an object
from eye at which the object can
clearly seen without causing strain
to the eye is called as least distance
of distinct vision (D) or distance of
distinct vision (DDV)
Magnifying power of simple microscope
“The magnifying power of convex lens or a simple
microscope is defined as the ratio of angle subtended by
the image at the eye (β) when seen through lens, to the
angle subtended by the object at the eye (α) when the
object is held at the distance of distinct vision and seen
directly.”
1
1
AB AB A B AB AB&
AP D A P AP u
Magnifying power of simple microscope is,
AB / uMP
AB / D
DMP (11)
u
a = = b= = =
b= =
a
= - - - - - -
1 1 1But
f v u
Applying new Cartesian sign conventions
1 1 1 1 1
f ( v) ( u) v u
1 1 1
u f v
Multiplying the above relation by D we can write
D D D
u f v
D DMP
f v
= -
= - =- +- -
= +
= +
= +
1 1MP D
f v
If the image is formed at distance of distinct vision
i.e. V D then
D D DMP 1
f
:
v fWherepispower of lens
If the image is formed
DP
at infinity
i.e. v then
D DMP
f v
1
:
æ ö÷ç= + ÷ç ÷çè ø
=
= + = + =
=¥
=
+
+ =
Case 1
Case 2
D D D
f fMP DP
+ =¥
=
Compound Microscope
Magnifying power of compound microscope“Magnifying power of compound microscope is defined as “ratio of angle subtended at the eye by final image (β) to the angle subtended at the eye by the object (α) when placed at DDV.”
If object is at DDV from objective then μ0 = D.
( )( )
b= a = =
a= = =
b
= =
=
=
1 1
e 0
1 1 e 1 1
e
01 1
0
e
e
e
0 e
A B AB ABand
u u D
A B / u A B DMP
AB / D ABu
vA BBut M
AB u
D& M
u
M.P. of compound microscope is,
MP M x M
0 e
0
0
0 e
0
0
: If final image is formed at infinity then,
: If the final image is formed at DDV th
MP M x M
.
1
MP M x M
e ,
1
n
Case 1
Case 2
ee
e
ee
e
DM
f
v DMP
u f
DM
f
v DMP
u f
0 0 0
0
0 0
0 0
0 0
0 0
0 0 0
0 0
0 0
0 0 0
0
0
1 1 1
multiplying by u
1
1
. . if image is at infinity0
0. . 1 is image is formed at DDV.
0 0
e
Butv u f
u u
v f
u u
v f
u u f
v f
v f
u u f
f DM P
u f f
f DM P
u f fe
Q.1Magnification of a simple microscope is given by
0
a. b.
1 c. d.
e
D f
f D
L DD
f f f
```Q.2 In normal adjustment, the magnifying power of a compound microscope is
given by
0 e
e 0
e
0 0 e
f fDa) b)
f L f
fL D Lc) d)
D f f f
Ans.:
Ans.:
D
f
0 e
D L
f f
astronomical refracting telescope.
Magnifying power of telescope
magnifying power of telescope is defined as it is a ratio of angle (β) subtended by the image at eye as seen through telescope to the angle (α) subtended by the object as seen directly.”
.
MP = β/α
0 e
0
e
0
e
AB ABtan and tan
f f
tanMP
tan
fABMP
f AB
fMP
f
a = b=
b=
a
= ´-
=
Reflecting Telescope
Lenses are in series combination
1 1
2 1
1 1 1 2
1 2
1 2
1 2 3
1 1 11
&
1 1 12
1 2
1 1 1 1 1 1
1 1 1 1
1 1 1
.
1 1 1 1
f v u
f v v
Adding and
v u v v f f
v u f f
f f f
For nno of lenses
f f f f
Mirror Equation
From Fig. and are similar
' ' '
' ' '.......1
Since ’ ’, the ’ ’ and are also similar.
' ' '...2
Comparing eq. 1 and eq. 2 we get
' '
A B B F
MP PF
A B B For MP AB
AB PF
A B B P
AB BP
B F B P
PF BP
A B F MPF
APB A PB A B P ABP
But, –
' '
From Fig. B’P v , PF
1 1 1
f , BP u
( )
...(3)
B P PF B P
PF BP
v f v
f u
v f v
f u
v f vor
f u
v u for
B F B P PF
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