Geometric Optics

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Geometric optics is an optical model that describes the propagation of light in terms of rays. In geometric optics, the rays of light are important to approximately determine the paths along which light propagates under certain conditions.

There are some assumptions of geometric optics, which are:

  • Light rays propagate in a straight line path while traveling in a transparent medium.

  • Light rays bend at the interface of two with different refractive indexes. Light rays also split under certain circumstances.

  • Light rays follow a curved path in a medium of changing refractive index.

  • Light rays can be absorbed, reflected, and refracted.

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Light Geometric Optics cannot explain the properties of light like diffraction and interference. This simplification is useful in practice. 

Light Geometric Optics is an excellent way to describe the behavior of light as its wavelength is extremely small as compared to the size of the object that light deals with.

The Geometric Optics is significantly useful to describe the geometric aspects of imaging like optical aberrations.


What is Geometric Optics?

Light can behave in many ways as it has dual nature. It has wave nature and also particle nature in the form of a photon. 

Light travels in a straightline & this property of light is called rectilinear propagation of light. Geometrical optics primarily deals with the rectilinear propagation of light and phenomena like reflection, refraction, and polarization.

Geometrical optics is also called ray optics. It is a model of optics that describes the rectilinear propagation of light in terms of rays. In geometric optics, the path of the propagation of light in a straight line is determined by studying the rays of light.

For convenience, optics is divided into two sections based on the size of the objects with which light interacts. When light interacts with an object that has a wavelength much greater than the wavelength of light, then the behavior of light is like that of a ray, and it doesn't display its wave nature. This is the part of optics, which is called “geometric optics”.


Refraction of Light Through a Prism Experiment

Our Objective

  1. To study the angle of deviation ‘d’, and find the angle of minimum deviation ‘D’ from the i-d curve for an angle of incidence ‘i’.

  2. To find the refractive index of the material of prism by using A (angle of the prism) and D.

Theory

Prism

A prism is an optical device. It is made up of polished flat surfaces that refract light. A prism that has a triangular base and rectangular sides is called a triangular prism.

A prism is usually made from materials like glass, plastic, and fluorite. A prism is used to split white light into its constituent components.


How a Prism Works?

When there is a transaction of light from one medium to another medium, it gets refracted by an angle. The angle of refraction of light depends on the angle of incidence, which the incident ray makes with the surface of the prism, and it also depends on the ratio between the refractive indices of the two media. 

This is called Snell's law and is given by:

n = sin i/sin r                           

Where,

i = angle of incidence

n = refractive index of the material of the prism

r = angle of refraction.

Different wavelengths of light refract differently, and the refractive index varies with the wavelength of light used. Light of different color (or wavelength) refract differently and emerge from the prism with different angles. This is called dispersion. 

This property is that light can be used to separate a single beam of light into its constituent colors.

The relation between Refractive Index ‘n’, Angle of Minimum Deviation ‘D’ and Angle of Prism ‘A’ can be learned here below:

Consider the following triangular prism.

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The two refractive surfaces of the given prism are ABFE and ACDE, respectively. The angle between them, angle ‘A’ is the angle of the prism.

A ray of light through prism undergoes two refractions while passing through the prism. 

Let KL be a monochromatic beam of light that falls on the side AB of the prism. It gets refracted traveling along the path LM. At the point M it undergoes refraction once again and emerges out along MN. 

The angle of deviation can be stated as the angle where the emergent ray deviates from the extending direction of the incident ray.

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If there is a rise in the angle of incidence, then the angle of deviation ‘d’ decreases and reaches a minimum value. 

The angle of deviation increases if the angle of incidence is further increased.

A graph is drawn by taking the angle of incidence ‘i’ in the X-axis, and the angle of deviation ‘d’ along the Y-axis. 

The graph obtained is a curved graph.

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The angle of minimum deviation is calculated from the graph. Let D be the angle of minimum deviation. The refractive index ‘n’ of the material of prism is calculated by using the formula.

N = (sin (A+D)/2)/sin A/2


Do You Know?

Do you know what relative refractive index is?

The relative refractive index can be defined as the ratio of the speed of light in one medium to that of the speed of light in another medium.

FAQ (Frequently Asked Questions)

Q1. Why is Geometric Optics important?

Ans- We can better understand the phenomena like reflection and refraction by geometric optics. The use of instruments like mirrors, lenses, prism, and fibers are based on geometric optics.

Q2. What do you mean by Ray Optics?

Ans- Ray optics is the other name for geometric optics. Light rays always propagate in a rectilinear path. When light travels through space, its amplitude oscillates (like other waves).

Q3. What is the difference between Physical Optics & Geometric Optics?

Ans- Geometric optics studies the optical properties of light like refraction and reflection, whereas, physical optics work on the principle of wave nature of light.

Q4. Explain Dispersion through a Glass Prism.

Ans- 

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From the fig shown above, the white incident light has been split by the prism into its constituent colors.

  • The various colors that emerge from prism are arranged in an order called ‘VIBGYOR.’

  • The name VIBGYOR is taken from the first letters of all the following colors:

                    V − Violet

                    I − Indigo

                    B − Blue

                    G − Green

                    Y − Yellow

                    O − Orange

                    R – Red

  • The band of the colored components of light is called the spectrum of light.

  • Dispersion is the phenomenon of splitting of light into its constituent colors or wavelengths.