What is the diameter of the hole if the width of the central maximum is 4.3 cm and the distance between the aperture and the screen is 4.0 m?
The diameter of the hole can be calculated using the formula:
Diameter of the hole = (1.22 × λ × L) / w
Given Data:
- He-Ne laser wavelength, λ = 633 nm
- Distance between aperture and screen, L = 4.0 m
- Width of central maximum, w = 4.3 cm
Calculating the diameter of the hole:
1. Convert 4.3 cm to meters: 4.3 cm = 0.043 m
2. Substitute the values into the formula:
Diameter of the hole = (1.22 × λ × L) / w
Diameter of the hole = (1.22 × 633 × 10⁻⁹ × 4.0) / 0.043
Diameter of the hole = (3.84 × 10⁻⁶) / 0.043
Diameter of the hole = 89.302 μm
Therefore, the diameter of the hole is 89.302 μm.
Understanding the Calculation:
The central maximum width and the distance between the aperture and the screen are crucial factors in determining the diameter of the hole through which the He-Ne laser light passes. The formula utilized takes into account these variables along with the laser wavelength.
When the central maximum width is 4.3 cm and the distance to the screen is 4.0 m, the diameter of the hole is calculated to be 89.302 μm. This calculation involves unit conversion and substitution of values into the formula mentioned earlier.
It is essential to accurately calculate the diameter of the hole to ensure the proper functioning of the optical system. Understanding the relationship between these parameters allows for precise adjustments and optimal performance.
In conclusion, the diameter of the hole plays a significant role in determining the characteristics of the light passing through it. By utilizing the formula and given data, the calculation results in a diameter of 89.302 μm.