Interference effects are produced at point P on a screen as a result of direct rays from a 485 nm source and reflected rays off the mirror. If the source is 94 m to the left of the screen, and 1.02 cm above the mirror, calculate the distance y to the first dark band above the mirror
To calculate the distance y to the first dark band above the mirror, we need to consider the interference effects produced by the rays from the source and the reflected rays off the mirror.
Interference occurs when two or more waves overlap. In this case, the direct rays from the source and the reflected rays off the mirror are interfering with each other.
The distance y to the first dark band above the mirror can be found using the equation for the path length difference (PLD) between the direct and reflected rays:
PLD = 2d
Here, d represents the distance from the point of observation (P) to the mirror.
To find d, we can use the Pythagorean Theorem:
d² = (distance from source to screen)² - (distance from source to mirror)²
Let's plug in the given values:
(distance from source to screen) = 94 m
(distance from source to mirror) = 1.02 cm = 0.0102 m
d² = (94 m)² - (0.0102 m)²
Now we can calculate d:
d = √[(94 m)² - (0.0102 m)²]
Once we have the value of d, we can use the formula for the path length difference:
PLD = 2d
The distance y can be calculated by using the wavelength (λ) of the light as a reference:
y = PLD * (wavelength / 2π)
Here, λ = 485 nm = 485 × 10^(-9) m
Now we can substitute the values and calculate y:
y = (2d) * (wavelength / 2π)
Remember to convert the wavelength to meters for accurate calculations.
Keep in mind that these calculations may involve some approximations and assumptions, so the exact answer may vary slightly.