Class 12 Physics Chapter 9 Ray Optics Notes

Ray Optics

Nature Of Light

Light is a form of energy that makes object visible to our eyes. Newton believed that light consisted of a stream of particles, called corpuscles. Huygens proposed wave theory of light. This theory could explain the phenomena of interference, diffraction, etc. Thomas Young, through his double slit experiment, measured the wavelength of light.
Maxwell suggested the electromagnetic theory of light. According to this theory, light consists of electric and magnetic fields, in mutually perpendicular directions, and both are perpendicular to the direction of propagation. Heinrich Hertz produced in the laboratory the electromagnetic waves of short wavelengths. He showed that these electromagnetic waves possessed all the properties of light waves.
Light travels in vacuum with a velocity given by
c=1μ0ε0√=3×108m/s
where μ0 and ε0 are the permeability and permittivity of free space (vacuum).
The magnitudes of electric and magnetic fields are related as
EB=c
In 1905, Albert Einstein revived the old corpuscular theory using plank’s quantum hypothesis and through his photoelectric effect experiment showed that light consists of discrete energy packets, called photons. The energy of each photon is
E=hf=hcλ
At present, it is believed that light has dual nature, i.e., it has both the characters (wave-like and particle-like).

Electromagnetic Spectrum

The visible light (λ=4000 Å to λ=7500 Å) forms only a very small range of the total electromagnetic spectrum, as shown in figure. Beyond violet region, there are ultraviolet rays,
χ-rays and γ-rays. Beyond red region, there are infrared rays and radio waves.
Seven colours in the visible light, in increasing order of wavelength, are Violet, Indigo, Blue, Green, Yellow, Orange and Red (VIBGYOR).

Characteristic of Eye

Eye is most sensitive to yellow-green light (λ=5500 Å). The persistence of eye is (1/16) second. It means that the impression of light pulse remains on the retina of the eye for (1/16) second. If time interval between two successive light pulses is less than (1/16) s, eye cannot distinguish them separately.
The colour sensation of eye is determined by frequency of the light wave and not by its wavelength.

Light Waves

Like any other wave, for light-waves also, the velocity c, the frequency f and wavelength λ are related as
c=fλ
Therefore, the frequency range of visible light is

For violet : fmax=cλmin=3×108m/s4000A∘=3×1084×10−7=7.5×1014Hz

For red : fmin=cλmax=3×108m/s7500A∘=3×1087.5×10−7=4×1014Hz

Thus, the optical frequencies are of the order of 1015 Hz. The speed of light of all wavelengths in vacuum is same (= 3 x 108 m/s). However, in a medium the speed of light is different for different wavelengths,
υ∝λ
When light passes from free space to any other medium, its speed reduces. The denser the medium, the lesser is the speed of light in it. On entering another medium, the velocity and the wavelength of the light may change, but its frequency (and hence its colour) remains the same.

Optics

Optics is the study of the properties of light, its propagation through different media and its effects. In most of the situations, the light encounters objects of size much larger than its wavelength. We can assume that light travels in straight lines called rays, disregarding its wave nature. This allows us to formulate the rules of optics in the language of geometry, as rays of light do not disturb each other on intersection. Such study is called geometrical (or ray) optics. It includes the working of mirrors, lenses, prisms, etc. When light passes through very narrow slits, or when it passes around very small objects, we have to consider the wave nature of light. This study is called wave (or physical) optics.  

Reflection of Light

When light strikes the surface on an object, some part of the light is sent back into the same medium. This phenomenon is known as reflection. The surface, which reflects light, is called mirror. A mirror could be plane or curved.

Laws of Reflection

(i) The incident-ray, the reflected-ray and the normal to the reflecting surface at the point of incidence all lie in the same plane.
(ii) The angle of reflection is equal to the angle of incidence (i = r)

If i = 0, then r = 0. It means a ray incident normally on a boundary, after reflection it retraces its path.
The angle made by the incident ray with the plane reflecting surface is called glancing angle. Thus, the glancing angle = 90° – i.

Real and Virtual Objects

The object for a mirror can be real or virtual. If the rays from a point on an object actually diverge from it and fall on the mirror, the object is said to be real. And if the rays incident on the mirror appear to converge to a point, then this point is said to be virtual point object for the mirror.

Real and Virtual Images

If the reflected (or refracted) rays actually meet at a point, this point is the real image. And if the reflected rays do not actually meet but only appear to diverge from a point, this point is the virtual image.The real image can be obtained on a suitably placed screen, but virtual images cannot.

Angle of Deviation (δ)

Angle of deviation δ is defined as the angle between directions of incident ray and emergent ray. So, if light is incident at an angle of incidence i,
δ=180∘−(i+r)=180∘−2i

Reflection from a Plane Surface

When a real object is placed in front of a plane mirror, the image is always erect, virtual and of same size as the object. It is at same distance behind the mirror as the object is in front of it.If an object moves towards (or away from) a plane mirror at speed v, the image will also approach (or recede) at same speed v. Thus, the speed of the image relative to the object will be v – (–v) = 2v.
Keeping the incident ray fixed, if the mirror is rotated through an angle θ,about an axis in the plane of mirror, then the reflected ray rotates through an angle 2θ.Lateral Inversion

The image formed by a plane mirror suffers lateral-inversion. That is, in the image the left is turned into the right and vice-versa with respect to object. Thus, as shown in figure, the letter 'd’ will appear as ‘b’. However, the mirror does not turn up and down. Actually, the mirror reverses forward and back in three-dimensions (and not left into right).
If we keep a right-handed coordinate system in from of a plane mirror, only the z-axis is reversed. This way, a plane mirror changes right-handed co-ordinate system (or screw) to left-handed.

Two Identical Plane Mirrors

If two plane mirrors are inclined to each other at 90°, the emergent ray is always antiparallel to the incident ray if it suffers one reflection from each (as shown in figure) whatever be the angle of incidence. The same is found to hold good for three-plane mirrors forming the corner of a cube, if the incident light suffers one reflection from each of them.
If two plane mirrors are inclined to each other at an angle θ, the number n of images of a point object formed is determined as follows:
(i) If 360∘θ is an even integer (ray m),

n = m – 1 (for all positions of the object)

(ii) If 360∘θ is an odd integer (say, m),

n = m (when the object is not on the bisector of mirrors)
n = m – 1 (when the object is on the bisector of mirrors)

(iii) If 360∘θ is a fraction,

n = the integral part of the fraction

Note that
(1) If an object is placed between two parallel mirrors (θ=0∘), the number of images formed will be infinite.
(2) All the images lie on a circle with radius equal to the distance between the object O and the point of intersection of the mirrors C.
(3) The number of images formed may be different from the number of images seen (which depends on the position of the observer)

Application 1

A ray of light is incident at an angle of 30° with the horizontal. At what angle with horizontal must a plane mirror be placed in its path so that it becomes vertically upwards after reflection ?

Solution

Suppose that a plane mirror is kept horizontal as shown in Fig. (A). The reflected ray will make an angle of 30° with horizontal, or an angle of 60° with the vertical.To make the reflected ray to go vertically upwards, it is required to be rotated about O counterclockwise by 60°. To achieve this, therefore, the plane mirror is required to rotate about O by half the angle, i.e., by 30°, as shown in Fig. (B).