Problem 94 - College Physics

Question

If the entire slab (without the oil) is submerged in a fluid with an index of refraction of \(1.5,\) what will be the effect? A. The slab will appear to change color. B. Light striking the slab could be totally reflected. C. The slab will be very difficult to see. D. Light exiting the slab could be totally reflected.

Step-by-Step Solution

Answer

C. The slab will be very difficult to see.

Step 1: Understand the Problem

We need to determine the effect on a slab submerged in a fluid with a refractive index of 1.5. This involves understanding how light behaves at interfaces between two different media.

Step 2: Consider the Optical Properties

Lasers or light waves are affected by changes in the refractive index. When a slab is submerged in a medium with a similar refractive index, the change of direction of light (refraction) is minimized.

Step 3: Evaluate Each Option

- Option A: Change in color is related to different wavelengths being absorbed or reflected, not the refractive index directly. - Option B and D: Total internal reflection occurs when light travels from a medium with a higher refractive index to a lower one, which is not the case here as the slab is in a fluid with equal or higher refractive index. - Option C: For a slab fully submerged in a medium with a similar refractive index, light does not bend significantly; thus, it makes the slab difficult to see.

Step 4: Select the Correct Answer

Given that the refractive index of the slab and fluid is similar, the bend and reflection of light are minimized, leading to the slab being difficult to see. Therefore, the correct answer is C. The slab will be very difficult to see.

Key Concepts

Refractive Index

The refractive index is a fundamental concept in optics that describes how light propagates through different media. It is defined by the equation \[ n = \frac{c}{v} \]where \( n \) is the refractive index, \( c \) is the speed of light in a vacuum, and \( v \) is the speed of light in the medium. This index indicates how much the speed of light is reduced inside a medium compared to a vacuum.
For example, a refractive index of 1.5 means that light travels 1.5 times slower in that medium than in a vacuum. Different materials have unique refractive indices, influencing how light behaves as it travels through them.

• Higher refractive index means light slows down more.
• The refractive index affects how light bends or refracts at the interface of two materials.

In the given exercise, both the slab and the surrounding fluid have a similar refractive index, which results in minimal bending of the light, making it difficult to observe the slab clearly.

Total Internal Reflection

Total internal reflection is a phenomenon that occurs when a light ray hits a boundary between two media and is completely reflected back into the initial medium. For this to happen, light must travel from a medium with a higher refractive index to one with a lower refractive index. There is a critical angle, specific to the media involved, above which total internal reflection occurs.
If the angle of incidence exceeds this critical angle, the light does not pass through to the other medium but instead reflects entirely back into the original medium. This is the principle behind the workings of fiber optic cables and many optical devices.

• Total internal reflection requires a higher to lower refractive index transition.
• It involves a specific critical angle for complete reflection.

In the context of our exercise, since the refractive index of the surrounding fluid is not lower than that of the slab, total internal reflection cannot occur, ruling out options B and D.

Light Refraction

Light refraction refers to the bending of light as it passes from one medium to another with a different refractive index. This change in direction results from a change in light speed as it enters a new medium.
Refraction is governed by Snell's Law, given as:\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]where \( n_1 \) and \( n_2 \) are the refractive indices of the first and second media, respectively, and \( \theta_1 \) and \( \theta_2 \) are the angles of incidence and refraction.

• Light bends towards the normal when it enters a medium with a higher refractive index.
• Less bending occurs with similar refractive indices between media.

This understanding explains why, in our exercise, the slab becomes difficult to see. With similar refractive indices, light refraction is minimal, reducing visibility of the slab in the fluid environment, supporting option C as the correct answer.