REFRACTION OF LIGHT | OPTICS

OPTICS | Part - 2| 

Refraction of light

STUDY NOTES 

For first part of optics 
Optics | Part -1 | Reflection of light 


Refraction of  Light :- 

Diagram of refraction of light

• When a ray of light is incident on the boundary between two transparent media, a part of it passes into the second medium it changes its direction. This phenomenon of light  is called refraction.
• As shown in figure above When a light ray enter in glass from air at the refractive surface light ray get deflected from its original path.

Laws of refraction of light:- 

1.  Incident ray , refracted ray and normal all lies in the same plane.
2. Snell's law :- 

Diagram of Snell's law for refraction of light

• Ratio of sin of incidence angle to sin of refracted angle is constant that is equal to refractive index of medium.

According to Snells law

nᵢsinθᵢ  = nᵣ sinθᵣ

sinθᵢ/sinθᵣ = nᵣ/nᵢ

sinθᵢ/sinθᵣ = ⁱnᵣ

where

• θᵢ = incidance angle
• θᵣ = refraction angle
• nᵢ = refractive index of first medium
• nᵣ = refractive index of second medium
• ⁱnᵣ = relative refractive index of medium 2 with respect to medium 1

refraction of light by rectangular glass slab:-  

Diagram of refraction of light from rectangular glass slab

Refraction by rectangular glass slab can be understand by two sub parts.

1. Refraction of light from air-glass  surface

2. Refraction of light from glass-air surface.

Refraction of light from air-glass surface:- 

When light ray goes from air ( rarer medium ) into glass ( denser medium) then it will bend towards normal.

That means in this case

Incidance angle > Refraction angle

Refraction of light from air-glass surface:- 

When incident light ray goes from glass ( denser medium) into air ( rarer medium) it will bends away from the normal after refraction of light. As shown in figure above.

That means in this case - 

Incidance angle < Refraction angle 

complete refraction of light by rectangular glass slab

Refractive index :- 

Absolute refractive index :- 

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

μ = v/c

where 

• c = speed of light in vacuum
• v = speed of light in the medium.
• μ = absoulte refractive index.

relative refractive index

relative refractive index of a medium is defined by the ration of refractive of that medium to refractive index of another medium.

for example 

relative refractive index of glass with respect to water can be defined as 

ʷμᵍ = μᵍ/ μʷ

Where 

•  μᵍ = absoulte refractive index of glass
• μʷ = absoulte refractive index of water

Thin lens

• A thin lens is defined as a portion of transparent refracting medium bounded by two surfaces. One of the two surfaces must be curved. 
• Following figures show a number of lenses formed by different refracting surfaces.
• A lens is one of the most familiar optical devices for a human being. 
• A lens is an optical system with two refracting surfaces.
• The simplest lens has two spherical surfaces close enough together that we can neglect the distance between them (the thickness of the lens). We call this a thin lens.

Convex lens ( Converging lens)

• this lens is thick from centre and thin from edges as shown in figure. 
• It is also called converging lens because it converges parallel beam of light at focus after refraction of light.
• It can form both real and virtual image for real object.
• Focal length for convex lens is always positive.
• Power of convex lens is always positive.

Uses of Convex lens :- 

1. In magnifying glass

2. In cameras 

3. In spectacles (to overcome long sightedness)

4. In binoculars 

 2. Concave lens ( Diverging lens)

• This lens is thin from centre and thick from edges. 
• It is a diverging lens because it diverges parallel beam of light after refraction of light.
• Focal length of concave lens is always negative.
• Power of concave lens is always negative.
• Image formed by concave lens is always virtual and eract.

Uses of concave lens :- 

1. In spectacles (to overcome short sightedness)

2. Peepholes in door 

Some inportant definations to lens :- 

1. Centre of curvature (C1 and C2 ) : The two bounding surfaces of a lens are each part of a complete sphere. The centre of the sphere is the centre of curvature.
2. Radius of curvature (R1 and R2) : The radii of the curved surfaces forming the lens are called radii of curvature.
3. Principal axis : The line joining the two centres of curvature is called principal axis.
4. Optical centre : A point on the principal axis of the lens from which a ray of light passes undeviated.
5. Principal foci : There are two principal foci of a lens.
6. First principal focus F1 : It is a point on the principal axis, such that a ray, diverging from the point or converging towards the point, after refraction becomes parallel to principal axis.
7. Second principal focus F2 : It is a point on principal axis, such that a ray moving parallel to principal axis, after refraction converges or diverges towards the point.
8. Focal Length : The distance between optical centre and second principal focus is focal length. 

Sign conventions for spherical lens :- 

Image formation by spherical lens :- 

1. A ray parallel to the principal axis after refraction passes through the principal focus or appears to diverge from it.
2. A ray through the optical centre P passes undeviated because the middle of the lens acts like a thin parallel- sided slab
3. A ray passing through the first focus F1 become parallel to the principal axis after refraction.

Image formation by convex lens :- 

1. When object is at infinity:- 

Properties of image :- 

• Real , point sized.
• At focus.

2. When object is placed beyond 2F :- 

Properties of image:- 

• Real, inverted 
• Diminished in size.
• Between f2 and 2f2.

3. When object placd at C1.

Properties of image:- 

• Real,inverted 
• Same in size.
• At C2.

4. When object is placed between F1 and C1:- 

Properties of image:- 

• Real, inverted 
• Magnified in size.
• Beyond C2.

5. When object is placed at F1 :- 

Properties of image:- 

• Real, inverted 
• Extremely enlarged 
• At infinity

6. When object is placed between F1 and O :- 

Properties of image:- 

• Virtual and erect 
• Enlarged in size.
• Between F1 and C1.
• Same side of object.

Image formation by concave lens :- 

1. When object is at infinity:- 

Properties of image:- 

• Virtual  and erect 
• At Focus 
• Point sized 

2. When object is placed anywhere infront of concave lens.

Properties of image:- 

• Virtual and erect 
• Between F1 and O.
• Smaller in size.

Lens maker formula :- 

• Consider an object O placed at a distance u from a convex lens as shown in figure. Let its image I after two refractions from spherical surfaces of radii R1 (positive) and R2 (negative) be formed at a distance v from the lens. Let v1 be the distance of image formed by refraction from the refracting surface of radius R1. This image acts as an object for the second surface. Using,

• This expression relates the image distance v of the image formed by a thin lens to the object distance u and to the thin lens properties (index of refraction and radii of curvature). It is valid only for paraxial rays and only when the lens thickness is much less then R1 and R2. The focal length f of a thin lens is the image distance That corresponds to an object at infinity. So, putting u = infinity and v = f in the above equation, we have

This is lens maker formula.

• it can be used to determine the values of R1 and R2 that are needed for a given refractive index and a desired focal length f.
• Combining eqs. (iii) and (v), we get

Which is known as the lens formula. 

Magnification of lens :- 

Power of a lens:- 

By optical power of an instrument (whether it is a lens, mirror or a refractive surface) we mean the ability of the instrument to deviate the path of rays passing through it. If the instrument converges the rays parallel to the principal axis its power is said positive and if it diverges the rays it is said a negative power.

Combination of lens:- 

Cutting of lens :- 

1. A symmetric lens is cut along optical axis in two equal parts. Intensity of image formed by each part will be same as that of complete lens.
2. A symmetric lens is cut along principle axis in two equal parts. Intensity of image formed by each part will be less compared as that of complete lens. (aperture of each part is 2/1 times that of complete lens)

■■■■■■■■■■■

Finish 

Thank you for reading

Coming soon

Next part of optics 

OPTICS | Part -3 | Refraction  of light  by Prism

□□□□□□□□□□