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# Angle of Deviation Prism

Angle of deviation prism is an important tool to calculate the angle of deviation. Two important principles are involved in understanding the concept of angle of deviation prism, which are as follows:-

• Reflection and
• Refraction.
The second concept is more important to understand the angle of deviation prism.  This concept is actually occurred in the prism when the ray of light is passed into the prism.  In terms of refraction we can easily describe the angle of deviation prism.  Basically the total amount of refraction in ray of light through a prism when a ray of light is passed through the prism is usually expressed in terms of the main subject that is angle of deviation. If we will describe in a detailed way then its definition is as follows:-

“It is defined as the angle between the incident ray of a light which is entering in the first face or side of the prism and the refracted ray that is coming out from the second face or side of the prism.”

To understand the angle of deviation in prism it is important to understand why the refraction occurs in the prism. The simple answer is because of difference in velocity of light inside and outside of the prism. By inside and outside, we mean that the rarer medium and denser medium respectively. In the rarer medium the velocity of light is always higher than the denser medium.  In the case of prism air is the rarer medium and prism itself is denser medium. So when a ray of light is entering inside the prism, then the speed of the light decreases and hence it is refracted that is bending with some angle. So this is basic phenomenon to understand the concepts of angle of deviation in prism.

It is also important to note that the angle of deviation in prism varies with the wavelength. This is because the refraction indices are different for different wavelengths. So in the visible light spectrum, the colors which have longer wavelength deviates more. And the colors which have shorter wavelength deviates less.  So it is clear that there are various concepts which need to be understood before understanding the angle of deviation in prism. Two more important points which we shall now as follows:-

• Speed of light in vacuum or air = 3 x 10 ^8 m/s.
• Speed of light in prism = 2 x 10 ^8 m/s (approximately)
This difference of speed of light in vacuum or prism is actually related to the phenomenon refraction which in turns related to the angle of deviation prism. If this difference is not there then there would not be any refraction and finally there will not be any term like angle of deviation.

At last it is important to note that the angle of deviation can be calculated or it can be measured with the help of spectrometer. And also it is important to note that with the help of formulas and laws of refraction one can easily find the angle of refraction also.

From Wikipedia

Prism (optics)

In optics, a prism is a transparent optical element with flat, polished surfaces that refractlight. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use "prism" usually refers to this type. Some types of optical prism are not in fact in the shape of geometric prisms. Prisms are typically made out of glass, but can be made from any material that is transparent to the wavelengths for which they are designed.

A prism can be used to break light up into its constituent spectralcolors (the colors of the rainbow). Prisms can also be used to reflect light, or to split light into components with different polarizations.

## How prisms work

Light changes speed as it moves from one medium to another (for example, from air into the glass of the prism). This speed change causes the light to be refracted and to enter the new medium at a different angle (Huygens principle). The degree of bending of the light's path depends on the angle that the incident beam of light makes with the surface, and on the ratio between the refractive indices of the two media (Snell's law). The refractive index of many materials (such as glass) varies with the wavelength or color of the light used, a phenomenon known as dispersion. This causes light of different colors to be refracted differently and to leave the prism at different angles, creating an effect similar to arainbow. This can be used to separate a beam of white light into its constituent spectrum of colors. Prisms will generally disperse light over a much larger frequency bandwidth than diffraction gratings, making them useful for broad-spectrum spectroscopy. Furthermore, prisms do not suffer from complications arising from overlapping spectral orders, which all gratings have.

Prisms are sometimes used for the internal reflection at the surfaces rather than for dispersion. If light inside the prism hits one of the surfaces at a sufficiently steep angle, total internal reflection occurs and all of the light is reflected. This makes a prism a useful substitute for a mirror in some situations.

### Deviation angle and dispersion

Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the element and using Snell's law at each interface. The exact expressions for prism deviation and dispersion are complex, but for small angle of incidence \theta_0 and small angle \alpha they can be approximated to give a simple formula. For the prism shown at right, the indicated angles are given by

\begin{align}

\theta'_0 &\approx \frac{n_0}{n_1} \theta_0 \\ \theta_1 &= \alpha - \theta'_0 \\ \theta'_1 &\approx \frac{n_1}{n_2} \theta_1 \\ \theta_2 &= \theta'_1 - \alpha \end{align}. For a prism in air n_0=n_2 \simeq 1. Defining n=n_1, the deviation angle \delta is given by

{\delta = \theta_2 + \theta_0 \approx n \theta_1 - \alpha + \theta_0 = n \alpha - n \theta'_0 - \alpha + \theta_0 \approx (n - 1) \alpha}

The dispersion \delta (\lambda) is the wavelength-dependent deviation angle of the prism, so that for a thin prism the dispersion is given by

\delta (\lambda) \approx [ n (\lambda) - 1 ] \alpha

## Prisms and the nature of light

In Isaac Newton's time, it was believed that white light was colorless, and that the prism itself produced the color. Newton's experiments convinced him that all the colors already existed in the light in a heterogeneous fashion, and that "corpuscles" (particles) of light were fanned out because particles with different colors traveled with different speeds through the prism. It was only later that Young and Fresnel combined Newton's particle theory with Huygen's wave theory to show that color is the visible manifestation of light's wavelength.

Newton arrived at his conclusion by passing the red color from one prism through a second prism and found the color unchanged. From this, he concluded that the colors must already be present in the incoming light â€” thus, the prism did not create colors, but merely separated colors that are already there. He also used a lens and a second prism to recompose the spectrum back into white light. This experiment has become a classic example of the methodology introduced during the scientific revolution. The results of this experiment dramatically transformed the field of metaphysics, leading to John Locke's primary vs secondary quality distinction.

Newton discussed prism dispersion in great detail in his book Opticks. He also introduced the use of more than one prism to control dispersion. Newton's description of his experiments on prism dispersion was qualitative, and is quite readable. A quantitative description ofmultiple-prism dispersion was not needed until multiple prism laser beam expanders were introduced in the 1980s.

Cuboid

In geometry, a cuboid is a solid figure bounded by six faces, forming a convex polyhedron. There are two competing (but incompatible) definitions of a cuboid in the mathematical literature. In the more general definition of a cuboid, the only additional requirement is that these six faces each be a quadrilateral, and that the undirected graph formed by the vertices and edges of the polyhedron should be isomorphic to the graph of a cube. Alternatively, the word â€œcuboidâ€� is sometimes used to refer to a shape of this type in which each of the faces is a rectangle (and so each pair of adjacent faces meets in a right angle); this more restrictive type of cuboid is also known as a right cuboid, rectangularbox, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped.

## General cuboids

By Euler's formula the number of faces (F), vertices (V), and edges (E) of any convex polyhedron are related by the formula "F + V - E" = 2 . In the case of a cuboid this gives 6 + 8 - 12 = 2; that is, like a cube, a cuboid has 6 faces, 8 vertices, and 12 edges.

Along with the rectangular cuboids, any parallelepiped is a cuboid of this type, as is a square frustum (the shape formed by truncation of the apex of a square pyramid).

## Rectangular cuboid

In a rectangular cuboid, all angles are right angles, and opposite faces of a cuboid are equal. It is also a right rectangularprism. The term "rectangular or oblong prism" is ambiguous. Also the term rectangularparallelepipedor orthogonal parallelepiped is used.

The square cuboid, square box, or right square prism (also ambiguously called square prism) is a special case of the cuboid in which at least two faces are squares. The cube is a special case of the square cuboid in which all six faces are squares.

If the dimensions of a cuboid are a, b and c, then its volume is abc and its surface area is 2ab + 2bc + 2ac.

The length of the space diagonal is

d = \sqrt{a^2+b^2+c^2}.\

Cuboid shapes are often used for boxes, cupboards, rooms, buildings, etc. Cuboids are among those solids that can tessellate 3-dimensional space. The shape is fairly versatile in being able to contain multiple smaller cuboids, e.g. sugar cubes in a box, small boxes in a large box, a cupboard in a room, and rooms in a building.

A cuboid with integer edges as well as integer face diagonals is called an Euler brick, for example with sides 44, 117 and 240. A perfect cuboid is an Euler brick whose space diagonal is also an integer. It is currently unknown whether a perfect cuboid actually exists.

Question:If the apex angle of your prism had been significantly lower, say around 15 , how would the DATA and the RESULTS of the experiment have changed? Explain your reasoning. "DATA" is the angle of minimum deviation and "RESULTS" is the index of refraction. How will these change?

Answers:Data will obviously change as A/2 is the angle of refraction on one face and A has changed. Naturally A+dm will also change. Bu the result ill not change because it is tech property of the material ansd depends velocity of light in it and has nothing to do with the shape of the medium.

Question:If a white ray is passing at minimum Deviation through a prism, it disperses int the VIBGYOR. Out of these dispersed chromatic rays, which one would be parallel to the base of the prism?

Answers:Hello George, congrats. A thought provoking query is made by you. The angle of the prism is one the factors to be considered. Say our prism is equilateral prism. Hence A = 60 deg. The refractive index of the material of the prism depends on the wavelength of the radiation passing through. So recalling the expression mu = sin {( A+D)/2}/ sin A/2, the value of D which suits well for mu and A, will be the minimum deviation for that particular colour. Hence that particular coloured ray would go parallel to the base of the prism. One more clue. We know angle of incidence i = A+D / 2. After setting for minimum deviation for the spectrum of colours of white light, with the given i and A, D could be calculated. The colour which has this calculated D will go parallel to the base of the prism. Lastly usually we rely on the yellow colour as the mean colour. So mostly yellow of the spectrum of white light will go parallel to the base of the prism.

Question:This triangular prism is irregular. The height is 2 cm. One side is 10 cm, second side is 6cm and the third side is 8cm. It has a 90 degrees angle. How to find it's area?

Answers:Figure each side separately. Figure the base separately. add them together. Since there is a 90 angle, the base must be a Right angle. A of Right angle is bh 2 Sides appear to be scalene angles. So, side side Base: (10cm 6 cm) / 2 = 30cm Sides: (10cm 2cm)/2 = 10cm ...........,(6cm 2cm)/2 = 6cm ............(8cm 2cm)/2 = 8cm 30+10+6+8 = 54cm