OPTICS

Chapter 9 . Optics

(Science of light)

Page No.

Section

Topic

159

9.2

Nature of light

159-161

9.3

Ray optics & Geometrical optics

162

9.4.2

Reflection from curved mirrors

166-167

9.6.1

Application of Tot.internal Reflection

167

9.7

Refraction from spherical surface &

lenses

175-179

9.9 9.10

Natural Phenomenon, Defects lenses

180-184

9.11

Optical Instruments

Omitted portions

https://youtu.be/cTuIbx9tZa0

SPHERICAL ABERRATION

When the rays are farther from the
principal axis, the focus gradually shifts
towardspole. This phenomenon (defect)
arises due to spherical shape of the
reflecting surface, hence
as spherical aberration. It results into a
blurred image with unclear boundaries.

In the case of curved mirrors, this defect
can be completely eliminated by using a
parabolic mirror. Hence surfaces of mirrors
used in a search light, torch, headlight of a car,
telescopes, etc., are parabolic and not spherical.

Refraction

If a ray of light comes to an
interface between two media
and enters into another
medium of different refractive
index,it changes itself suitable
to that medium. This
phenomenon is defined as
refraction of light

Absolute Refractive Index

Absolute refractive index of a medium is defined as the ratio of speed of light in vacuum to that in the
given medium.

Light travels fastest in
Vaccum.

Relative refractive Index

A crane flying 6 m above a still clear water lake sees a fish underwater. For the crane, the fish appears to be 6 cm below the water surface. How much deep should the crane immerse its beak to pick that fish?
For the fish, how much above the water surface does the crane appear?
Refractive index of water = 4/3.
Solution: For crane, apparent depth of the fish is 6cm and real depth is
to be determined.
For fish , real depth is to be determined.

Total Internal Reflection

●At a particular angle of incidence ic in the denser medium, the corresponding angle of refraction in the rarer medium is 00 .

● For angles of incidence greater than ic, the angle of refraction
become larger than 900 and the ray does not enter into rarer medium
at all but is reflected totally into the denser medium. This is called
total internal reflection.

Define Critical angle.
Critical angle for a pair of refracting media can be defined as that angle of
incidence in the denser medium for which the angle of refraction in the rarer
medium is 900 .

For any thin lens

Refraction at a single spherical surface

●Consider a spherical surface
YPY’ of radius curvature R,
separating two transparent
media of refractive indices n1
and n2 respectively .

●The ray OP along the
principal axis travels
undeviated along PX.
Another ray OA strikes the
surface at A.

X

A

N

●Angle of incidence in the medium n1 at A is i.

●As n1 < n2 , the ray deviates towards the normal, travels along AZ and cuts
the principal axis at I. Thus, real image of point object O is formed at I.

● Angle of refraction in medium n2 is r.

●
According to Snell’s law,
n1sin(i) = n2r sin (r )
●Let 𝜶, 𝞫, 𝛄 be the angles subtended by incident ray, normal and
refracted ray with the principal axis.

●

Lens maker’s equation

Consider a lens of radii of curvature R1 and R2 kept in a medium such that n is
refractive index of material of the lens with respect to the medium.
Assuming the lens to be thin, P is the common pole for both the surfaces. O is a
point object on the principal axis at a distance u from P.
First refracting surface of the lens of radius of curvature R1 faces the object.

Axial ray OP travels undeviated. Paraxial
ray OA deviates towards normal and would
intersect axis at I1, in the absence of second
refracting surface. PI1 = v1 is the image distance
for intermediate image I1.

becomes

Before reaching I1, the ray PI1 is intercepted at B by the second refracting surface.
I1 acts as virtual object for second surface of radius of curvature (R2) and object distance
is u = v1 .
As the incident rays are in the medium of refractive index n, this is the medium of
(virtual) object ∴􀀃
n1 = n and refractive index of the other medium is n2 = 1.

After refraction , the ray bends away from the normal and intersects the principal axis
at I which is the real image of object O formed due to the lens. ∴􀀃PI = v.

Adding we get,

This is called lens
makers’

Dispersion of light

PRISM FORMULA

P

M

Q

A
T

M’

R

S

N

X

The figure shows principal section ABC of a prism of
absolute refractive index n kept in air.

Refracting surfaces AB and AC are inclined at
angle A, which is refracting angle of prism or
simply ‘angle of prism’. Surface BC is the base.
A monochromatic ray PQ obliquely strikes first
reflection surface AB.
Angle of incidence at Q is i, angles of refractio at Q and
R are r1 and r2.

B

C

This is PRISM FORMULA

Thin Prism

Prisms having refracting angle less than 100 are called thin prisms.
For such prisms sin 𝚹≅𝚹.

𝜹༌= A (n-1)

Angular Dispersion

Dispersive Power

Ability of an instrument to disperse constituent colours is its dispersive
power.