Showing posts with label Critical Angle. Show all posts
Showing posts with label Critical Angle. Show all posts

Ray Optics Complete Lesson

Light is a form of energy. It exhibits a wide variety of properties. If the size of the object is much larger than the wavelength of the light, light appears like travelling in straight lines. It exhibits certain properties under these conditions and that properties are studied and rename called Ray optics.

In Ray optics we study about reflection, refraction, dispersion and the deviation. 

Reflection is the phenomena of light bouncing back into the same medium after striking a boundary that is separating the two media.

Refraction is the phenomenon of light due to which light travels into the other medium after striking a boundary that is separating the two media.

Dispersion is the phenomenon of splitting up of a white light into multiple colors when it is passed through a prism. 

Deviation is the phenomena of changing its path when the light is passing through a different media.

In this chapter we are also going to study regarding mirrors, lenses, prisms, critical angle, total internal reflection, microscopes and telescopes.


This post is a list of all the topics in Ray optics which includes problems and solutions.

No comments:
Labels: , , , , , , , ,

Problems and Solutions on Refraction of Light Through Prism

Problem and solution

A ray of light is incident normally on one of the faces of the prism of prism angle 30° and known refractive index. What is the angle of the deviation of the light ray in this case?

As the light ray is striking the first surface normally, angle of incidence and angle of refraction at that surface are equal to 0.

It is proved that the angle of the prism is equal to the sum of angle of refraction and angle of incidence inside the prism. Also basing on the deformation of the refractive index at each of the surface we can derive the equation for the deviation of the light ray experienced as shown.



Problem and solution

A ray of light is incident normally on one of the refracting surfaces of a prism of known angle of the prism. The emergent ray grazes the other refracting surface. What is the refractive index of the material of the prism?

As the incident Ray is normal to the first surface, angle of incidence and angle of refraction at the first surface is equal to 0. Hence angle of the prism is equal to the angle of incidence of the light ray at the second surface inside the prism.

As the light ray is grazing the boundary at the second surface we can use the definition of the critical angle and solve the problem as shown below.




Problem and solution

A light ray passes through a prism of known refractive index experience minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. The angle of the prism is ?

As the prism is in minimum deviation condition, angle of incidence is equal to angle of emergence and angle of refraction at the first surface is equal to angle of incidence at the second surface. Taking these things into consideration and the formula of the refractive index, we can derive the equation and the value for the angle of the prism as shown below.



Problem and solution

One of the refracting surfaces of the prism of angle 30° is silvered. A ray of light incident at an angle of 60° at one of the surface of the prism has retraced its path. What is the refractive index of the material of the prism?

Retracing of light is possible only when the angle of incidence at the second surface is equal to 0.

That implies angle of the prism is nothing but equal to angle of refraction at the first surface of the prism. Basing on the definition of refractive index as the ratio as the sin angle of incidence to the sin angle of emergence at any of the given surface,we can calculate the value as shown below.





Related Posts

4 comments:
Labels: , , , , ,

Problems and Solutions on Critical angle and Total internal Reflection

When a light ray moves from denser medium to rarer medium, it moves away from the normal. This is just because the different mediums are having different refractive index. When there is a change of media, the wavelength and the velocity of the light changes. As a consequence its path is also modified. With respect to the increase of angle of incidence, angle of refraction also increases.

At a particular angle of incidence, the refracted light ray grazes the boundary that is separating the two media. This particular angle of incidence is called critical angle. If the angle of incidence is more than the critical angle, the light ray reflects back into the same medium. This phenomenon is called total internal reflection.

Problem and solution

A ray of light travelling in a transparent medium of known refractive index , falls on the surface separating the medium at an angle of incidence of 45°. Find the value of the refractive index at which the light ray experience total internal reflection?

We know that for the total internal reflection, the angle of incidence shall be more than that of critical angle. Taking the very basic concept of this into consideration,we can solve the problem as shown below.



Problem and solution

The speed of light into different media is given. A ray of light enters from medium 1 to medium 2 it and angle of incidence i. If the light ray suffers total internal reflection, what is the value of angle of incidence?

As it is explained earlier, whenever there is a change of medium there will be a change of wavelength as well as the velocity of light. Frequency is the characteristic property of the source and it remains constant even when there is a change of medium.

Here in this problem being the media are different the refractive index is also automatically different. For the total internal reflection to happen, the light ray shall always moves from denser medium to rarer medium. Velocity of the light is more in the rarer medium and less in the denser medium. Velocity of light is maximum in vacuum because that is the rarest medium. The refractive index of vacuum is treated as one.

Basing on the definition of the total internal reflection we can write refractive index of the denser medium to rarer medium as shown. Being frequency is constant, the ratio of refractive index of the two media is inversely proportional to their respective velocities of light.

The solution to the problem is as shown below.



Problem and solution

If a ray of light in the denser medium strikes a rarer medium and angle of incidence, the angle of reflection and angle of refraction are given. If the reflected and the reflected light rays are at right angles to each other, the critical angle for the given pair of the media is how much?

As the light ray is moving from denser medium to rarer medium angle of refraction is more than that of angle of incidence. After striking the boundary some portion of the light reflects back into the same medium and some another portion of the light refracts to the other medium.

It is given in the problem that the reflected and the reflected light rays are at right angles to each other. By applying the basic mathematics and the definition of the critical angle with can solve the problem as shown below.


Problem and solution

A beam of light consists of red, green and blue colors. This light incidents on the right angled prism as shown. The refractive indices of the materials of the prism for the different colors are given. Find the color which will be separated from the other colors?

As each color has different refractive index, each color will have different critical angle when it is passing through the same glass prism. For the color which has an angle of incidence is more than the critical angle of the prism, there will be total internal reflection. It is clear basing on the deformation of the critical angle that for the total internal reflection to happen the refractive index of the color shall be greater than 1.414.

Basing on the values of the refractive indices it is clear that green and blue colors experience total internal reflection and the red refracts into the other medium.




Related Posts

1 comment:
Labels: , , ,

Applications of Total Internal Reflection

Optical fibre

It is a optical device which helps in communicating the signal from one place to another place without any transmission loss. It works basing on total internal reflection concept.

It has two cylindrical parts where inner one is called core and the outer one is called cladding. The refractive index of core is more than that of cladding.

In this device light Ray moves from denser medium to rarer medium. We shall allow the light Ray to incident in the denser medium in such a way that at the surface it shall experience total internal reflection. We shall pass the light Ray into the system with a particular angle so that after going into the device it will experience total internal reflection. This particular angle is called angle of launching.

When the light is passed through optical fibre there is no wastage of energy takes place. The entire input that is given at one end will automatically reach the other end. It is simply because the entire message is restricted itself only to the denser medium. As angle of incidence is more than critical angle the entire light Ray reflects back into the core itself. Thus no portion of the energy has gone into the cladding and hence there is no wastage of energy.

Optical Fibre is a very thin, light weighted and a flexible device. It is a part of a nanotechnology such that the size of this device is very small. Hundreds of optical fibres tied together will just take the size of a small pipe.

With different angles of launching, we can pass multiple signals through a single optical fibre simultaneously. This different signals takes different parts and hence there is no messing up. They will reach two different destinations without any problem.



Formation of Mirage

Mirage is nothing but the illusion of a object seen in reverse that is inverted that when we see it from  long distance during the summer seasons.This happens because of total internal reflection.

When a observer is standing at a distance and seeing an object like a tree, he is seeing through the air. Direct light rays from the object becomes little bit difficult when the object is far away. The light rays from the object are reflected by the air layers that are there on the surface of the earth towards the observer. Being the summer, the air layers will have different temperatures. The air that is close to the surface of the earth is higher than the upper layer. 

As a result the lower layer is a rarer medium and upper layer is a denser medium. As a light Ray is trying to pass from denser medium to rarer medium, at a particular angle of incidence with experience a total internal reflection. As a result the light Ray reflects back to the observer as shown in the diagram. For the observer the light rays are extended through the eye is the reverse direction to see the formation of the image of the object. Thus the object appears like a inverted one for the observer and this phenomena is called a mirage.



The duration of the sun visibility

When there is no atmosphere around the Sun we can see it both in the morning and the evening straight from the origin. But there is a lot of atmosphere around the Sun and it is exposed to different temperatures. It is very clear that the air layer that is close to the surface of the earth will be that lesser temperature than the upper layer. Hence the lower layers behave like a denser medium and the upper layers behaves like a rarer medium. The phenomena of the total internal reflection take place here also. Hence we can see the sun even after the sun set was happened.



Total internal reflection in a prism

Basing on the definition of the total internal reflection and the critical angle, we can calculate the value of the critical angle of a glass prism as shown below. As the refractive index of the glass with respect to Air is close to 3/2, the corresponding critical angle is close to 42°.

If the angle of incidence through one of the face of the prism is more than 42°, then the light experience a total internal reflection as shown.




Related Posts

No comments:
Labels: , , ,

Critical Angle and Total Internal Reflection

Critical angle

When a light ray is moving from denser medium to rarer medium, it moves away from the normal. As the angle of incidence increases, angle of deviation also increases.

With the increase of angle of incidence angle of reflection in this case also increases. At a particular angle of incidence, angle of refraction becomes 90° and the light Ray grazes the boundary that is operating the two media. This particular angle of incidence is called critical angle. At the critical angle light Ray, goes exactly on the surface of the line separating the two media. Therefore at the critical angle angle of refraction is 90°. The reflected light rail is neither going into the rarer medium nor staying in the denser medium.

Total internal reflection

When a light ray is moving from denser medium to rarer medium, it moves away from the normal. With the increase of angle of incidence, angle of refraction also increases. For a particular angle of incidence called critical angle, angle of refraction is 90° and the light Ray just grazes the boundary that is separating the two media.

If the angle of incidence is more than the critical angle, the angle of refraction is more than 90°. Therefore even after the refraction the entire light Ray is reverted back into the denser medium.

The phenomena of the light restricting back into the denser medium when the angle of incidence is more than the critical angle is called total internal reflection. For the total internal reflection to happen there shall be two conditions satisfied.

The first condition is the light ray shall be moving from denser medium to a medium. The second condition is the angle of incidence shall be more than that of the critical angle.

Basing on the definition of the refractive index we can write a small equation for the critical angle as shown below.




Field vision of a fish

Let us consider a fish at a depth h from the surface of water. The fish would like to observe the surroundings in air media above the water. Hence it starts passing the light rays from the water into the air that is from denser medium to rarer medium.

The fish is able to see the surroundings above the surface of water until its angle of incidence is less than equal to critical angle. Once if the angle of incidence crosses the critical angle, the entire light rays are reflected back into the water. This is due to the phenomena of total internal reflection. Therefore the fish is able to see the surroundings only until the angle of incidence is equal to critical angle. Taking this concept into consideration and by some simple mathematical equations we can derive the equations for the Field vision of a fish as shown below.

Once if we are able to calculate the radius up to where the fish can see, we can calculate the area of the vision and that area is called Field vision of fish.



Related Posts

No comments:
Labels: , , ,
Subscribe to: Comments (Atom)