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When light passes through a narrow slit, it creates a diffraction pattern characterized by alternating bright and dark bands known as maxima and minima. The width of the slit plays a pivotal role in determining the spacing between these bands. By understanding how slit width influences diffraction, we can calculate the width of the slit using the given parameters.

The formula typically used for calculating the slit width in a single-slit diffraction pattern is:
\[ a \sin(\theta) = m \lambda \]where:

• \(a\) is the slit width.
• \(\theta\) is the angle of diffraction for the m-th minimum.
• \(m\) is the order number of the minimum (m = 1 for the first minimum).
• \(\lambda\) is the wavelength of the light.

Because small-angle approximation is often valid in optics, especially when the angle is small, we can approximate \(\sin(\theta)\) with \(\tan(\theta)\), which equals \(x/f\), where \(x\) is the distance from the central maximum to the first minimum and \(f\) is the focal length of the lens.

Thus, the slit width \(a\) can be derived as:
\[ a = \frac{\lambda f}{x} \]This allows us to plug in all known values to find the slit width in meters.

The wavelength of light is a fundamental concept in understanding diffraction patterns. It refers to the distance between successive peaks of a wave and is usually measured in nanometers (nm) for visible light. In this problem, the wavelength of green mercury light is provided as\(545 \text{ nm}\).

For computational purposes, it can be converted to meters by using the conversion,
\(1 \text{ nm} = 10^{-9} \text{ m}\).Therefore, the wavelength in meters is \(545 \times 10^{-9} \text{ m}\).

The wavelength of light affects how much the light diffracts as it passes through a slit. A longer wavelength means more diffraction, resulting in a more spread-out pattern, whereas a shorter wavelength creates a pattern closer to the slit. This property impacts the equation we use to determine the distance between the diffraction fringes, further affecting the calculation for the slit width.

Focal length is a measurement of how strongly a lens focuses or defocuses light. It is the distance between the lens and its focal point, the spot where light rays converging through the lens converge into a focus. The focal length in our problem is given as \(60 \text{ cm}\), which can be converted to meters by noting that\(1 \text{ cm} = 0.01 \text{ m}\), so it's equal to \(0.60 \text{ m}\).

This focal length is crucial for calculating the angle of diffraction using the relationship between the physical distance from the central maximum to the first minimum and the angle \(\theta\) in the diffraction formula.

In practical problems, especially those involving diffraction through slits, knowing the focal length allows us to use simple geometry and trigonometry. Essentially, the focal length helps bridge the physical measurements (like the distance between maxima and minima) with theoretical equations (like those derived from the properties of waves and light). This makes interpretations and calculations relating to diffraction patterns accessible and accurate.