## Tuesday, January 27, 2015

### 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.

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