Problem 85 - Master Resource Book in JEE Main Physics

Question

What should be refractive index of a transparent medium to be invisible in vacuum? (a) 1 (b) \(<1\) (c) \(>1\) (d) None of these

Step-by-Step Solution

Answer

The refractive index should be 1 for the medium to be invisible in vacuum.

Step 1: Understand the Concept of Refractive Index

The refractive index of a medium, denoted as \( n \), is a measure of how much the speed of light is reduced inside the medium compared to the speed of light in a vacuum. It is defined as \( n = \frac{c}{v} \), where \( c \) is the speed of light in vacuum, and \( v \) is the speed of light in the medium.

Step 2: Analyze the Question for Conditions of Invisibility

For a medium to be invisible, light should pass through it without any deviation or scattering. This means that the refractive index of the medium must be the same as that of the surrounding environment. In vacuum, the refractive index is 1.

Step 3: Determine the Refractive Index for Invisibility in Vacuum

Since in a vacuum the refractive index is 1, for an object to be perfectly invisible, its refractive index must also be 1. This way, there is no change in the speed of light as it passes through the object compared to the vacuum.

Step 4: Conclude with the Correct Option

The answer is (a) 1, because a refractive index of 1 ensures that light behaves as if it is still in the vacuum, making the medium invisible.

Key Concepts

Invisibility in Vacuum

In the context of physics, achieving invisibility means that light passes through an object without any deviation or alteration. This relates to the object's refractive index, which must match that of its surrounding environment. In a vacuum, the refractive index is exactly 1. Therefore, to achieve invisibility in a vacuum, the refractive index of the material must also be 1.

Light traveling through such a material would move at the same speed as it does in a vacuum, with no refraction or reflection occurring. As such, the medium becomes "invisible" to an observer because the light does not change its path.

This concept is crucial not only in theoretical physics but also in real-world applications like camouflage or advanced optics design.

Speed of Light in Medium

The speed of light is a constant in a vacuum, known as "c," approximately equal to 299,792,458 meters per second. However, when light enters a medium other than a vacuum, this speed is reduced.

The refractive index, denoted by \( n \), helps us understand how much this speed is reduced. It is calculated using the formula \( n = \frac{c}{v} \), where \( c \) is the speed of light in a vacuum, and \( v \) is the speed of light in the medium.

• A refractive index of 1 means no reduction in speed.
• If the refractive index is greater than 1, light slows down.
• If it were possible for \( n \) to be less than 1, light would actually speed up, but this doesn't occur naturally in typical materials.

Understanding this concept is essential when studying the optical properties of various materials and designing lenses and other optical devices.

Optical Properties of Materials

Optical properties describe how a material interacts with light. These can include absorption, reflection, refraction, and transmission. Key among these is the concept of the refractive index, which we have already discussed.

Different materials have different refractive indices, which influence how light travels through them. For instance:

• Glass generally has a refractive index around 1.5, slowing light considerably compared to a vacuum.
• Water has a refractive index of about 1.33, causing light to bend as it enters or exits the substance.
• Air, being quite close to a vacuum, has a nearly identical refractive index of around 1.0003.

These properties are foundational to understanding phenomena such as lenses magnifying objects, prisms dispersing light into spectra, and optical fibers transmitting data over great distances.
Overall, the optical properties of materials are vital in fields ranging from telecommunications to astronomy.