Question

helium-neon laser light is sent through a 0.300-mm-wide single slit. what is the width of the central maximum on a screen from the slit? how far is the second dark band from the second maximum

Answer 1

The central maximum width is determined using the single-slit diffraction formula. The position of the second dark band from the second maximum is calculated using the same formula with appropriate values.

The central maximum width and the location of the second dark band from the second maximum in a single-slit diffraction pattern can be calculated using the single-slit diffraction formula. The central maximum width (W) and the position of the dark bands depend on the wavelength of the light (λ), the slit width (a), and the angle of observation (θ).

1. Central Maximum Width (W):

The formula for the central maximum width in a single-slit diffraction pattern is given by:

`\[ W = (2\lambda L)/(a) \]` where:

• W is the width of the central maximum.

• 
  `\( \lambda\)` is the wavelength of the light.

• L is the distance from the slit to the screen.

• a is the slit width.

2. Position of the Second Dark Band (y):

The distance from the central maximum to the
`\( m \)-th` dark band can be calculated using:

`\[ y_m = (m\lambda L)/(a) \]`

where:

• 
  `( y_m )` is the distance from the central maximum to the
  `\( m \)-th` dark band.

• (m) is the order of the dark band.

Given the helium-neon laser light, which has a known wavelength, and the slit width, you can plug in the values into these formulas to calculate the central maximum width and the position of the second dark band from the second maximum.