Question

Two lasers, one red (with wavelength 633.0 nm) and the other green (with wavelength 532.0 nm), are mounted behind a 0.150-mm slit. On the other side of the slit is a white screen. When the red laser is turned on, it creates a diffraction pattern on the screen. The distance y3,red from the center of the pattern to the location of the third diffraction minimum of the red laser is 4.05 cm. How far L is the screen from the slit? Express this distance L in meters to three significant figures.

Answer 1

To calculate the distance L between the screen and the slit, use the single-slit diffraction minimum condition combined with the known distance of the red laser's third minimum and its wavelength.

Step-by-step explanation:

The student is working on a Physics problem related to single-slit diffraction. To find the distance L between the screen and the slit, we can use the formula for the position of a diffraction minimum, y = L × tan(θ), where θ is the angle of the diffraction minimum. However, for small angles (as in most diffraction problems), tan(θ) ≈ sin(θ), so the formula simplifies to y = L × sin(θ). The condition for the minima in a single-slit diffraction pattern is given by a × sin(θ) = m × λ, where a is the width of the slit, m is the order number of the minimum, and λ is the wavelength of the light. Given that the third diffraction minimum (m = 3) for the red laser is at a distance y3,red = 4.05 cm from the pattern's center, and the wavelength of the red light is λ = 633.0 nm, we can write 0.150 mm × sin(θ) = 3 × 633.0 nm. Solving for sin(θ) and then using y = L × sin(θ) where y = 4.05 cm, we can calculate the distance L.