Optics II

Laws of Refraction
Total Internal Reflection
Image Formation By Convex Lens & Concave Lens
In a homogeneous medium, light rays travel in a staight line. Whenever a ray of light passes from one transparent medium to another, it gets deviated from it's original path while crossing the interface of the two media (expect in normal incidence).

This phenomenon of deviation or bending of light rays form their original path while passing from one medium to another is called refraction.

In the second medium, the ray either bends towards the normal ar away from the normal with respect to its path in the first medium.

If the refracted ray bends towards the normal with respect to the incident ray, then second medium is said to be optically denser as compared to the first medium.









If the refracted ray bends away from the normal, then the second medium is said to be optically rarer as compared to the first medium.

Law of Refraction














The phenomenon of refraction takes place according to the following two laws:

1. The incident ray, the refracted ray and the normal to the surface of refraction at the point of incidence, all lie in one plane.

2. The ratio of the sine of angle of incidence ‘i’ to the sine of angle of refraction ‘r’ is a constant for a given pair of media and for light of a given colour.

If the angle of incidence and angle of refraction be i and r respectively, then



This law is called Snell's law.

Principle of Reversibility of Light

A ray travelling along the path of the reflected ray is reflected along the path of the incident ray.

In the same way a refracted ray reversed to travel back along its path will get refracted along the path of the incident one. Thus, the incident and refracted rays are mutually reversible. This is called the principle of reversibility of light.

When a ray of light travels from first medium to the second medium, we have



When the path of the ray is reversed, it travel from medium-II to medium-I.

Using Snell's law, we have



Total Internal Reflection

If a ray of light travelling in a denser medium strikes a rarer medium at an angle of incidence i which is greater than the critical angle C , it gets totally reflected back into the same medium.
This phenomenon is called as 'total internal reflection'.












Condition For Internal Reflection :

There are two essential conditions for total internal reflection:

1 The ray of light should travel from a denser medium to a rarer medium.

2 The angle of incidence in denser medium should be greater than the critical angle, i.e. i > C , for the pair of medium in contact.

Now, at this stage, we may define critical angle as the angle of incidence for which the angle of refraction in 90o .

Expression For Critical Angle






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Refraction Through Thin Lens

Lens : A lens is a transparent medium bounded by two refracting surfaces such thet at least one of the refracting surfaces is curved.

Types of lenses: Broadlly, lenses are of the following types:

(a) Positive Lenses: Positive lenses produce a real image, - the image produced by this type of lens can be projected onto a screen.

The three basic positive lenses are :

(1) Double Convex lens
(2) Plano - Convex lens
(3) Positive Meniscus lens


(b) Negative Lenses: Negative lenses do not bring parallel light rays together, they do not produce a real image, but they do produce a virtual image.

The three basic negative lenses are :

(1) Double Concave lens
(2) Plano - Concave lens
(3) Negative Meniscus lens

Some Important Definations:




(i)
Optical center : Optical center is a point for a given lens through which any ray passes undeviated.

(ii) Principal axis : The line joining the center of the curvature of the two bounding surfaces is called principal axis.

(iii) Principal Focus(F) : When a beam of light is incident on a lens in a direction parallel to the principal axis of the lens, the rays after refraction through the lens converge to (as in case of convex lens) or appear to diverge (as in case of concave lens) from a point on the principal axis as shown below, This point F is called principal focus of the lens.

(iv) Focal length : The distance between optical centre and focus is called focal length. It is denoted
by f.

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Image Formation By Convex Lens

(i) When the object is at infinity


(ii) When the object lies beyond C (i.e.,between infinity and C)

(iii) When the object lies at C

(iv) When the object lies between F and C

(v) When the object at F

(vi) When the object lies between P and F

Image Formation By Concave Lens

(i) When the object is in front of the lens

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