Which one of the following statements is correct regarding the travel of a light beam from a rare to a dense medium?
A light beam travelling from a rare medium to a dense medium slows down and bends towards the normal.
Understanding Light Travel from Rare to Dense Medium
When a light beam travels from one transparent medium to another, it changes direction. This phenomenon is called refraction of light. The extent to which light bends depends on the optical density of the two media.
What are Rare and Dense Media?
Media can be classified as optically rare or optically dense based on how they affect the speed of light. A medium is optically denser if the speed of light in it is less than in the other medium. Conversely, a medium is optically rarer if the speed of light in it is greater than in the other medium.
Optical density is related to the refractive index (\(\mu\)) of the medium. The refractive index is defined as the ratio of the speed of light in vacuum (\(c\)) to the speed of light in the medium (\(v\)):
\(\mu = \frac{c}{v}\)
A medium with a higher refractive index is optically denser, and light travels slower in it. A medium with a lower refractive index is optically rarer, and light travels faster in it.
Light Travelling from a Rare to a Dense Medium
Consider a light ray travelling from an optically rare medium (like air) to an optically dense medium (like water or glass).
- Speed of Light: When light enters a denser medium from a rarer medium, its speed decreases. This is because the light waves interact more with the particles in the denser medium.
- Bending of Light (Refraction): The light ray also changes direction. To describe the bending, we draw a line perpendicular to the surface separating the two media at the point where the light ray enters the second medium. This line is called the normal.
- Direction of Bending: When light travels from a rarer medium to a denser medium, it bends towards the normal.
This behavior is summarized by Snell's Law of Refraction, which relates the angle of incidence (\(\theta_1\)) in the first medium, the angle of refraction (\(\theta_2\)) in the second medium, and the refractive indices of the two media (\(\mu_1\) and \(\mu_2\)):
\(\mu_1 \sin(\theta_1) = \mu_2 \sin(\theta_2)\)
If medium 1 is rarer and medium 2 is denser, then \(\mu_2 > \mu_1\). For Snell's Law to hold, if \(\mu_2 > \mu_1\), then \(\sin(\theta_1) > \sin(\theta_2)\). Since sine increases with angle for angles between 0° and 90°, this implies \(\theta_1 > \theta_2\). The angle of incidence (\(\theta_1\)) is the angle between the incoming ray and the normal, and the angle of refraction (\(\theta_2\)) is the angle between the refracted ray and the normal. If \(\theta_2 < \theta_1\), the refracted ray is closer to the normal than the incident ray, meaning it bends towards the normal.
Analyzing the Options
Let's examine each statement provided in the options based on our understanding of light refraction:
- Option 1: "A light beam travelling from a rare medium to a dense medium slows down and bends towards the normal." This statement matches our explanation: speed decreases in a denser medium, and light bends towards the normal when going from rare to dense.
- Option 2: "A light beam travelling from a rare medium to a dense medium speeds up and bends towards the normal." This is incorrect because light slows down, not speeds up, when entering a denser medium.
- Option 3: "A light beam travelling from a rare medium to a dense medium slows down and bends away from the normal." This is incorrect because light bends towards, not away from, the normal when entering a denser medium. Bending away from the normal happens when light goes from dense to rare.
- Option 4: "A light beam travelling from a rare medium to a dense medium speeds up and bends away from the normal." This is incorrect on both counts: speed decreases, and it bends towards the normal.
Based on the analysis, only the first statement correctly describes what happens when a light beam travels from a rare medium to a dense medium.
Revision Table: Light Refraction Summary
| Travel Direction | Change in Speed | Bending Direction |
|---|---|---|
| Rare to Dense | Decreases (Slows down) | Towards the Normal |
| Dense to Rare | Increases (Speeds up) | Away from the Normal |
Additional Information on Optical Density
It is important not to confuse optical density with mass density. Optical density is related to how much a medium opposes the passage of light (specifically, slows it down), which is quantified by the refractive index. While there is often a correlation (denser materials by mass tend to be optically denser), it is not always the case. For example, turpentine is less dense than water by mass but is optically denser.
Understanding the behavior of light when changing media is fundamental to many optical phenomena and devices, including lenses, prisms, and fiber optics.
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