Refraction at Spherical Surfaces

• Laws of refraction:

• Refraction describes how light bends when passing from one medium to another.

• Refractive index(n):

• The ratio of the speed of light in vacuum to its speed in a material is known as the refractive index of that material.

• It is a dimensionless quantity.

• Snell’s law:

• Snell’s Law describes how light is refracted at the boundary between two media.

• It is expressed as: $n_1 \sin \theta_i = n_2 \sin \theta_t$

• Where $n_1$ and $n_2$ are the refractive indices of the two media and $\theta_i$ and $\theta_t$ are the angles of incidence and refraction.

• Absolute Refractive Index:

• The ratio of the speed of light in vacuum (c) to the speed of light in the medium (v) is known as the absolute refractive index.

• Mathematically, it is represented as $$\eta=c/v$$

• Relative Refractive Index:

• It is the ratio of absolute refractive indices of two materials/media.

• Mathematically, $$n_{21}=n_2/n_1$$ Where $$n_{21}$$ is the relative refractive index of medium 2 with respect to medium 1 and $n_2$, $n_1$ are the absolute refractive indices of medium 2 and medium 1 respectively.

• Real and Apparent Depth:

• The actual distance from an object to the surface is called real depth whereas apparent depth is the perceived distance from the object’s surface to its image.

• Total Internal Reflection:

• Total Internal Reflection (TIR) happens when light passes from a denser medium to a rarer one and the incident angle is greater than a certain critical angle.

• This phenomenon is crucial in the working of optical fibers.

• Critical Angle:

• The angle of incidence for which the refracted angle becomes 90° is known as the critical angle.

• It is the minimum angle of incidence required for total internal reflection.

• Prism and Its Types:

• A prism is a transparent optical element with flat, polished surfaces that refract light.

• There are different types of prisms like triangular prisms, rectangular prisms, and more.

• Prisms are used in a wide range of optical applications such as dispersion of light, spectroscopy, and image processing.

• Dispersion of Light:

• It occurs when light of different wavelengths (colors) is refracted at different angles, causing the light to spread out into a spectrum.

• Prisms are commonly used to demonstrate this effect.

• Rainbow:

• A rainbow is a naturally occurring optical phenomenon that appears as a circular arc of distinct colors in the sky.

• It is caused by the dispersion of sunlight as it passes through raindrops.