Suppose you use the same double slit to perform Young's double-slit experiment in air and then repeat the experiment in water. Do the angles to the same parts of the interference pattern get larger or smaller? Does the color of the light change? Explain.

Short Answer

Expert verified
In conclusion, when performing Young's double-slit experiment in water compared to air, the angles to the same parts of the interference pattern get smaller due to the shorter wavelength of light in water. Additionally, the color of the light changes, shifting slightly towards the blue end of the spectrum, because of the difference in wavelengths between the two mediums.

Step by step solution

01

Recall the equation for the angle of maximum interference

First, we need to recall the equation for the angle of maximum interference in Young's double-slit experiment. For bright fringes the equation is given as: \(sin⁡θ = \frac{mλ}{d} \) Where θ is the angle for a bright fringe, m is the fringe number (order), λ is the wavelength of light, and d is the distance between the two slits.
02

Understand the impact of mediums (air and water) on the speed and the wavelength of light

When light passes from one medium to another, its speed and wavelength are affected by the refractive index of the medium; however, the frequency remains constant. As the speed of light in a medium is related to its refractive index (n) as follows: \(v = \frac{c}{n} \) Where v is the speed of light in the medium, c is the speed of light in a vacuum, and n is the refractive index of the medium. Since the refractive index of water is greater than that of air (n_water > n_air), the speed of light in water will be less than that in air (v_water < v_air). Now, let's look at the effect on the wavelength of the light in water. The relationship between frequency (f), speed (v), and wavelength (λ) is given as: \(v = fλ \) Since the frequency remains constant, the change in the speed of light will cause a change in the wavelength. Therefore, the wavelength of light in water will be shorter than in air (λ_water < λ_air).
03

Analyze the change in the angle of maximum interference and color of light in water compared to air

Now we can analyze how the angles of the interference pattern change and whether the color of light changes when moving from air to water. Using the equation for angle of maximum interference, we can compare the angles in air and water: \(sin θ_{air} = \frac{mλ_{air}}{d} \) \(sin θ_{water} = \frac{mλ_{water}}{d} \) Since \(λ_{water}< λ_{air}\) (as we deduced earlier), we can conclude that the angle of maximum interference in water is smaller compared to air (\(θ_{water} < θ_{air}\)). As for the color of light, when the wavelength of light changes, its color changes as well. Since the wavelength of light in water is shorter than in air, the color of light will appear slightly shifted towards the blue end of the spectrum. In conclusion, when performing Young's double-slit experiment in water compared to air, the angles to the same parts of the interference pattern get smaller, and the color of the light changes (shifts slightly towards the blue end of the spectrum).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free