Problem 84 - 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 to be invisible in vacuum.

Step 1: Understanding the Concept of Invisibility

For a medium to be invisible in vacuum, light must pass through it without any bending or reflection. This implies that the speed of light in the medium should be the same as in the vacuum.

Step 2: Recognizing Refractive Index in Vacuum

In a vacuum, the refractive index is defined as 1, since the speed of light is at its maximum and any other medium must have a refractive index relative to this.

Step 3: Equating Speeds for Invisibility

If we want light to travel through the medium as if it is still in vacuum, the speed of light in the medium must match the speed of light in vacuum. This means the refractive index of the medium should be equal to 1.

Step 4: Concluding the Solution

Since a medium with a refractive index of 1 would allow light to pass through without deviation, making the medium invisible in vacuum, the correct answer is (a) 1.

Key Concepts

Invisibility

Invisibility, in a scientific sense, is a phenomenon where light passes through an object without being absorbed, reflected, or refracted. This means the object does not cast a shadow or become visible to the eye. In the context of the refractive index, an object can become invisible if its presence does not alter the path of light passing through it.
When an object has a refractive index exactly equal to the surrounding medium (in this case, a vacuum), the light travels through both materials as if there was no change. Thus, the object appears invisible as there is no disruption in the light's behavior.

Vacuum

A vacuum is a space devoid of matter, where pressure is so low that air and other gas molecules are practically absent.
In such a space, the speed of light is at its maximum because there is no medium to cause resistance or slow it down. The refractive index of a vacuum is universally accepted as 1 and serves as a baseline for comparing how light behaves in different substances.

• Light moves in a straight line in a perfect vacuum.
• Refractive index in vacuum serves as a reference point when evaluating other media.

Speed of Light

The speed of light in a vacuum is approximately 299,792,458 meters per second and is denoted by the symbol \( c \). It is considered the ultimate speed in the universe. When light travels through a medium other than a vacuum, this speed decreases, which causes the light to bend.
The refractive index of a medium describes the ratio of the speed of light in vacuum \( c \) to the speed of light in the medium \( v \). This relationship is expressed by the equation \( n = \frac{c}{v} \), where \( n \) is the refractive index.
For a medium to be invisible in vacuum, the speed of light within that medium must match the speed in vacuum, requiring the refractive index to be \( n = 1 \).

Transparent Medium

A transparent medium is one through which light can pass without significant scattering, absorption, or reflection. Common examples include air, water, and glass, each with distinctive refractive indices.
A medium's transparency is crucial for invisibility. For a medium to be seen as invisible in a vacuum, its refractive index has to equal that of the vacuum. This implies that the light passes through it without any change in speed or direction.

• Uniformity in refractive index ensures no distortion in the transmission of light.
• In such media, because light does not bend or slow down, the effect of invisibility can be achieved, as there is no visual indication of the medium's presence.