# Refraction of light

### CONTENTS

Definition of refraction of wave

Refraction of  through rectangular glass block

Experimental determination of refractive index using real and apparent depth method

Laws of Refraction  waves

Refraction  through a triangular prism

Total internal reflection and Critical angle

Application of total internal reflection in nature

Application of totally reflecting prisms

Refraction  through lenses

Ray diagram construction for lenses

Lens formula

How to identify lenses

Power of lens

### Definition of refraction of light wave

Refraction of light is change in direction of light ray or wave when it travels from one medium to another of difference density. Refraction of light occurs when it travels from glass to air or from air to liquid and vice versa. The change in change in speed of light ray when it travels from one medium to another of difference is responsible for the refraction of light or bending of light ray

The parameter associated with refraction of light

Incident ray:  It is the path along which light travels in the first medium

Refracted ray: It is the path along which light travels in the second medium

Angle of incident: It is the angle the between the incident ray and normal

Angle of refraction: It is angle between the refracted ray and the normal

#### Refraction of light through rectangular glass block

In studying the refraction of light through a rectangular glass block above, we consider an incident ray of light which pass from air into the glass block and travel in new direction as refracted ray, and then come out as emergent ray, which is parallel to the incident ray. At this point we say that the incident ray has been refracted in the glass.

Read also: Reflection of light , Mirror formula

Note that there is also reflection at normal but is very weak, when compare to the refract ted ray

Real depth, apparent depth and refractive index

When you put object underneath a glass block, the object appear nearer to the top when viewed above.  So the distance of the object when observed from above is called apparent depth which is less than the real depth because of refraction  The depth of swimming pool also appear less than the real depth due to refraction

The real depth, apparent depth and refractive index is related mathematically as:

${ n=\frac { Real\quad depth }{ Apparent\quad depth } }$

Where n= refractive index

##### Experimental determination of refractive index using real and apparent depth method

Finding the refractive index of a glass block

AS shown on the image above, a straight line is ruled on a paper and glass block is placed vertically over the portion of the ruled line on paper. By the use of search pin attached to a piece of cork and held in clamp, the apparent height of the line is found by a no parallax method, moving the pin up and down until it coincides with the image of the of the line. Then the real and apparent depths are measured, and from it the refractive index of the glass is calculate us the relationship below. You can also determine the refractive index of water, using a glass cup and optical pin put inside

## Laws of Refraction light or waves

1. The first law of refraction of light or waves state that, the incident ray, refracted ray and the normal at the point of incidence, all lie on the same plane
2. The ratio of sine of the angle of incidence to the angle of refraction is equal to a constant which is called the refractive index of the second medium with respect to the first medium

${ n=\frac { Sin\quad i }{ Sin\quad r } }$

n=refractive index, i=angle of incidence, and r= angle of refraction of light

The second law of refraction of light or waves is also called Snell’s law

If a light travels from air to glass, according to the Snell’s law, the refractive index is given as

${ { _{ a }{ n }_{ g }=\frac { Sin\quad i\quad (air) }{ Sin\quad r\quad (glass) } } }$

The effects of refraction of light at plane surface

1. Apparent shallow depth of swimming pool
2. The apparent bending of stick when partial immersed in water

### Refraction of light through a triangular prism

From the diagram above a ray of light XY incident on face AB of the triangle, is refracted at y, and travels along YR in the glass and emerge on the face of the triangle AC, and moves along RS. It is also observed from the diagram above that the ray RS is not parallel to the ray XY

The angle between the original direction and final direction or the light ray is called angle of deviation. There also exist minimum angle of deviation, which is the smallest angle of deviation produced by the prism. At minimum deviation the light ray passes symmetrically through the prism. Therefore the refracted ray inside the prism makes equal angle with prism surface at Y and ay R

The refractive index can be given as

${ n=\frac { Sin\frac { 1 }{ 2 } ({ d }_{ m }+A) }{ Sin\frac { 1 }{ 2 } A } }$

A=refracting angle of the prism, dm=minimum deviation

Where n=refractive index, A=refracting angle of the prism and dm=minimum deviation

### Total internal reflection and Critical angle

From the diagram (A) above, a ray of light XY from air enter the glass and refracted at Y along YS. There is also reflection of light along YR, but is a very weak reflection.

Critical Angle

When the angle of incidence is increased the angle of refraction also increases, if you continue to increase angle of incidence, a point will reach when the corresponding angle of refraction will be 90o, at this point we say that the angle of incidence is the critical angle.

Now what is Critical angle?

Critical angle can be defined as the angle of incidence at which angle of refraction is 90o, when light passes a dense to less dense medium

Total internal reflection

At a point when the angle of refraction of light is 90o if the incident angle is increased to exceed the critical angle, there will be no refraction, but total internal reflection with strong reflected ray.

So total internal reflection of light occur when the critical angle is exceeded for light traveling from dense medium to less dense medium

Conditions for total internal reflection of light to occur

1. Light ray must be coming from dense medium to less dense medium
2. The angle of incident in denser medium must exceed the critical angle

The relationship between critical angle and refractive index

${ \frac { Sin\quad i }{ Sin{ 90 }^{ 0 } } ={ _{ a }{ n }_{ g } } }$

But sin90o=1, therefore

${ SinC=\frac { 1 }{ { _{ a }{ n }_{ g } } } }$

Where = critical angle

#### Application of total internal reflection of light in nature

1. Field view of fish under water: Fish under water can see object above the water surface only within a certain range, provided the water is unruffled. Fish can see everything above the water by rays which fall within a cone with half angle r=49o inside the water. Outside this cone the fish sees objects within the water by total internal reflection at the water-air boundary.
2. The mirage: When drive along a tarmac road on a hot day; you often seem to see a pool of water ahead of you. This pool disappears as soon as you come close and appear further ahead of you. This optical illusion , by which inverted images of palm tree or other distance objects often seen , sometimes as if it reflected from the ground is called The mirage is a phenomenon that can only be explained by total internal reflection

## Application of totally reflecting prisms

The totally reflecting prism or periscope binocular is used in submarine or ship instead of mirrors, because they can form one bright image of object, but mirror forms one bright and another second and weak image of an object, thereby creating confusion because at time the second image is as bright as the original image.

## Refraction of light through lenses

What is lens? A lens is a portion of a transparent medium bounded by two spherical surfaces or by a plane and a spherical surface

Refraction of light through lenses involves change in the direction of light rays as they travels from one medium to another, that is from less dense medium to denser medium or vice versa

Types of lenses

1. Convex or converging lens
2. Concave or diverging lens

Convex or converging lens: These lenses are thicker at the middle than at the edge. The converging lens makes ray of light originating from a point come together at another point called a focus.

When you look through a converging lens, you see a magnified and upright image. Also a magnified and inverted or diminished and inverted image could also be seen depending on the distance of image, from the other side of the lens.

The difference types of convex lens are shown below

Concave or diverging lens: These lenses are thinner at middle than at the edge. The diverging lens makes rays of light which passes through it to spread out or diverge. When we see through a diverging lens, we always see a diminished and upright image

The different types of diverging lenses are show in the diagram below

Lens Terms

1. 1. Principal axis of the lens: It is imaginary line joining the center of curvature of its surface

2.Principal focus  (F) of the a converging lens (convex lens): It is the point at which all rays parallel and close to the principal axis converge after refraction through the lens

1. Principal focus F of diverging lens (concave lens): It is the point at which a ray parallel and close to principal axis appears to diverge after refraction.
2. 4. Focus length (f): it the distance between the optical center and principal focus of the lens.

Note that the principal focus of the converging lens is not on the same side with the incident ray, but the principal focus of diverging lens is at the same side with incident ray though the ray do not actually pass through it.

## Ray diagram construction for lenses

For converging lens

(i).Object placed at a distance greater than 2f from the lens, the image is real inverted and smaller in size than object.

(ii).When Object is at 2f from the lens, the image is real, inverted and the same size with object.

(iii).If Object is at distance between 2f and f from the lens, the image is real, inverted and magnified

(iv).When Object at distance equal to f, the image is at infinity

(v).When Object is at distance less than f from the lens, the image is virtual, upright and magnified

For diverging lens

At any position of object from a diverging lens, the image remains, virtual, upright and diminished

# Lens formula

Where u=object height or distance, v=image distance or height, and f=focal length

${ m=\frac { image\quad height }{ Object\quad height } }$

Where m=magnification

# How to identify lenses

1. By feeling the lens with finger, if it is thinner at the center, the lens is diverging lens, but if it is thicker at the middle, the lens is a converging lens.
2. By bringing candle from a distance towards the lens, and looking through the lens, if the image is always erect and smaller than the candle , the lens is a diverging lens, but if the image is inverted and gradually increase in size as the candle is brought nearer, then disappear and reappear as enlarged and upright , the lens is converging lens
3. When a lens is pointed at a distant object and image appear on a screen, the lens if a converging lens.

# Power of lens

What is power of lens?

The power of lens can be defined as the reciprocal of the focal length expressed in meter

When the focal length of a lens is 1meter, the power of the lens is 1dioptre.

The power of lens in dioptre is given as

${ \frac { 100 }{ f(cm) } }$

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