Saurabh Koranglekar
Last Activity: 5 Years ago
To determine the angular width of the fringe in a double-slit experiment when the apparatus is immersed in water, we need to understand how the medium affects the wavelength of light and, consequently, the fringe patterns observed on the screen. The angular width of a fringe in a double-slit experiment can be calculated using the formula for angular width, which is given by: θ = λ / d where:- θ is the angular width,- λ is the wavelength of light,- d is the distance between the slits.When the apparatus is placed in a different medium, the wavelength of light changes according to the refractive index of that medium. The relationship is defined as: λ' = λ / n where:- λ' is the wavelength in the new medium,- n is the refractive index of the medium (for water, n = 4/3).Let's break this down step-by-step:
Step 1: Calculate the Wavelength in Water
The original wavelength of the light in air is given as 600 nm. To find the wavelength in water, we use the formula provided.
- λ = 600 nm = 600 x 10-9 m
- n (refractive index of water) = 4/3
- λ' = λ / n = (600 x 10-9 m) / (4/3) = (600 x 10-9 m) × (3/4)
- λ' = 450 x 10-9 m = 450 nm
Step 2: Calculate the New Angular Width
Next, we need to determine the angular width of the fringe using the new wavelength in water. We can use the same formula for angular width, but we need to adjust for the new wavelength.
- θ' = λ' / d
- Since the distance between the slits (d) remains unchanged, we can express the angular width in terms of the original width calculated in air. Since the fringe width is proportional to the wavelength, we can relate them:
- θ' = (λ' / λ) × θ
- θ = 0.2° (the original fringe width)
- θ' = (450 nm / 600 nm) × 0.2° = (0.75) × 0.2° = 0.15°
Final Result
Thus, the new angular width of the fringe when the entire experimental setup is immersed in water is 0.15°. This demonstrates how the medium can significantly affect the behavior of light and the resulting interference patterns. By understanding these principles, we can better appreciate the intricate nature of wave phenomena!
