Final answer:
The smallest separation between two slits for a second-order maximum in any visible light is 2L, where L is the distance between the slits and the screen.
Step-by-step explanation:
The smallest separation between two slits that will produce a second-order maximum for any visible light can be found using the equation for the position of the mth-order maximum in a double-slit interference pattern:
y = mλL / d
Where:
- y is the distance between the central maximum and the mth-order maximum
- λ is the wavelength of the light
- L is the distance between the slits and the screen
- d is the separation between the slits
Since we want to find the smallest separation between the slits, we need to consider the longest wavelength of visible light, which is approximately 760 nm. Plugging in the values, we have:
y = (2)(760 × 10^-9 m)(L) / d
To find the smallest separation between the slits, we want the position of the second-order maximum to be as small as possible. This occurs when y is the smallest possible value, which is equal to the distance between the slits:
d = (2)(760 × 10^-9 m)(L) / y
Therefore, the smallest separation between two slits that will produce a second-order maximum for any visible light is (2)(760 × 10^-9 m)(L) / (760 × 10^-9 m) or 2L.
For all visible light, the smallest separation between two slits that will produce a second-order maximum is 2L.