# Optics by lanyuehua

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```									                                              Optics

Reflection of Light

N
I                                              R

θ        θ

Laws of Reflection:

1) The angle of incidence is equal to the angle of reflection
2) The incident ray (I), the reflected ray (R) and the normal to the surface at the point of
incidence (N) lie in the same plane.

The image formed by a plane mirror is the same size as the object, is erect, and is located as far
behind the mirror as the object in front of it. In a plane mirror the image is perverted, i.e. right
and lift are interchanged with respect to the object.

Refraction of light:

Refraction is the change in direction of a light ray because of change of speed.

N
I

i
Medium 1
Air

Medium 2
Glass
r

R

For refraction we have also two laws:
Laws of Refraction:

1) For two given media,       = constant
Where, ’I’ is the angle of incidence and ‘r’ is angle of refraction.
This is known as a Snell’s law.
2) The incident ray (I), the refracted ray (R) and the normal to the surface at the point of
incidence (N) lie in the same plane.

From Snell’s Law

Where ,        refractive index of medium 2

refractive index of medium 1

refractive index (index of refraction) of medium 2 with respect to medium 1.

velocity of light in medium 1

velocity of light in medium 2

Absolute Refractive Index of a medium is

Total internal Reflection:

Light rays from an optically dense medium e.g. glass fall on a surface on the other side of which
is a less optically dense medium e.g. air. As the angle of incidence ‘ ’ is increased a situation is
reached in which the refracted ray points along the surface. That means the angle of refraction is
. In this case the incidence angle is called the critical angle . For angles of incidence larger
than this critical angle, no refracted ray exists, and we get total internal refraction.
Air

θ                 θ

Glass

We know,

Where      is the index of refraction of medium 2 with respect to medium 1. We also know,

As an example, let

Spherical Mirrors:

Concave mirrors and convex mirrors. The principal focus of a spherical mirror is the
convergence point for rays parallel to and close to principal axis of the mirror. It is located half
way between the mirror and its centre of curvature.

The mirror equation is:
u    object distance

v image distance

f focal length

The mirror equation applies to both concave and convex mirrors. The focal length f is taken as
positive for concave (converging) mirrors and negative for convex mirrors or diverging mirrors.
Real is positive and virtual is negative for object and images.

Magnification

When ‘m’ is negative the image is inverted and when ‘m’ is positive the image is erect.

Problem:

A candle is held 3.0cm from a concave mirror whose radius is 24cm. Where is the image of the
candle and what is its magnification?

Ans:

From the general mirror equation

So, the image is virtual.

Magnification

=1.33
So, the image is erect and magnified.

Images in a Concave Mirror:

When the object is:

1. At a distance greater than 2f in front of the mirror, the image is real, inverted and
diminished in size.
2. At a distance equal to 2f, the image is real, inverted and the same size as the object.
3. Between 2f and f, the image is real, inverted and magnified in size.
4. At a distance equal to f, no image is formed.
5. Nearer than f, image is virtual, erect and magnified.

Images in a Convex Mirror:

The image of any real object formed by a convex mirror is always virtual, erect and diminished.

Huygens’ Principle:

Take a point source of light S in air. The wave starts a S and travels outwards. After a time ‘t’ the
wave has travelled a distance ct. AB is the wave front. Now every point on this wave front may
be considered as a new or secondary centre of disturbance. The wavelet from A then reaches the
surface M of a radius ct and centre A after a time t.

M
A

ct
D
S
B

N
Huygens’ Principle can be stated as:

All points on a wave front can be considered as point sources for the production of spherical
secondary wavelets. After a time ‘t’ the new position of the wave front will be the surface of
tangency to these secondary wavelets.

Interference:

We know that light travels in straight line (reflection and refraction). However, interference and
diffraction are purely wave phenomena.

Newton thought light to be particle in nature whereas Huygens believed in the wave theory.
Thomas Young in 1801 performed the experiment where interference of light was observed. In
order to observe interference effects with light, the light from a single source is made to traverse
different optical paths to introduce a phase difference and then the beams are reunited.

A

S
Po
Source
P1
B
Dark

P2
Bright

Young’s Experiment

If the path difference between two waves is     the phase difference =2

Suppose for a path difference x, the phase difference is

For a path difference x, the phase difference =

Phase Difference =       x Path Difference
Constructive    interference      occurs     whenever     the   optical   path   difference
Destructive interference occurs whenever the path difference

Point   is equidistant from A and B. So   is bright.

We get bright fringes whenever there is constructive interference & dark fringes whenever there
is destructive interference.

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