Deviation Caused by Medium

When light travels from one medium to another, its speed changes, which can cause the light to bend. This bending of light is known as refraction. The deviation of light as it passes through different media is a fundamental concept in optics and is crucial for understanding phenomena such as the bending of light in lenses, prisms, and the atmosphere.

Refraction and Snell's Law

Refraction occurs because light travels at different speeds in different media. Snell's Law describes the relationship between the angles of incidence and refraction when considering the refractive indices of the two media.

Snell's Law is given by:

$$ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) $$

where:

• $n_1$ is the refractive index of the first medium
• $n_2$ is the refractive index of the second medium
• $\theta_1$ is the angle of incidence
• $\theta_2$ is the angle of refraction

The refractive index ($n$) of a medium is a dimensionless number that describes how much the speed of light is reduced inside the medium compared to the speed of light in a vacuum.

Deviation by a Prism

A prism is a transparent optical element with flat, polished surfaces that refract light. The deviation of light by a prism depends on the refractive index of the material and the angle of the prism.

The formula for the angle of deviation ($\delta$) by a prism is:

$$ \delta = (\theta_1 - \alpha) + (\theta_2 - \beta) $$

where:

• $\alpha$ is the angle of the prism
• $\beta$ is the angle of incidence inside the prism
• $\theta_1$ and $\theta_2$ are the angles of incidence and emergence from the prism

Factors Affecting Deviation

Several factors affect the deviation of light as it passes through different media:

• Refractive Index: The higher the refractive index, the greater the bending of light.
• Angle of Incidence: As the angle of incidence increases, the deviation generally increases until the light reaches the critical angle and undergoes total internal reflection.
• Wavelength of Light: Different wavelengths of light are refracted by different amounts, with shorter wavelengths (blue light) being refracted more than longer wavelengths (red light).
• Temperature: The refractive index of a medium can change with temperature, affecting the deviation of light.

Table of Differences and Important Points

Factor	Effect on Deviation	Description
Refractive Index	Direct Relationship	Higher refractive indices cause greater deviation.
Angle of Incidence	Complex Relationship	Deviation increases with the angle of incidence up to the critical angle.
Wavelength of Light	Inverse Relationship	Shorter wavelengths are deviated more than longer wavelengths.
Temperature	Varies with Material	Higher temperatures can decrease the refractive index, leading to less deviation.

Examples

Example 1: Refraction at a Single Boundary

Consider a light ray passing from air ($n_1 = 1.00$) into water ($n_2 = 1.33$) at an angle of incidence of $30^\circ$. Using Snell's Law, we can find the angle of refraction:

$$ 1.00 \sin(30^\circ) = 1.33 \sin(\theta_2) $$ $$ \sin(\theta_2) = \frac{1.00 \sin(30^\circ)}{1.33} $$ $$ \theta_2 = \arcsin\left(\frac{\sin(30^\circ)}{1.33}\right) \approx 22.09^\circ $$

Example 2: Deviation by a Prism

A prism with an angle of $60^\circ$ and a refractive index of $1.5$ has a light ray incident upon it. If the angle of incidence is $45^\circ$, we can calculate the deviation assuming the angle of emergence is equal to the angle of incidence (which is an approximation for small angles of incidence):

$$ \delta \approx 2(\theta_1 - \alpha) $$ $$ \delta \approx 2(45^\circ - 60^\circ) $$ $$ \delta \approx -30^\circ $$

The negative sign indicates that the light ray has deviated towards the base of the prism.

Understanding the deviation caused by a medium is essential for designing optical instruments, correcting vision, and analyzing natural phenomena like rainbows and mirages. It is also crucial for understanding the principles behind technologies such as fiber optics and lenses used in cameras and microscopes.