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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.

( )( )

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  

b= a = =

a= = =

b

= =

=

=

0 e

0

0

0 e

0

0

: If final image is formed at infinity then,

: If the final image is formed

MP M x M

.

1

MP M x M

1

at DDV then,

ee

e

ee

e

DM

f

v DMP

u f

DM

f

v DMP

u f

Case 1

Case 2

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

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