Question

A monochromatic light of wavelength 589 nm incident on a double slit with slit width 2.5μm and unknown separation results in a diffraction pattern containing nine interference peaks inside the central maximum. Find the separation of the slits.

Answer 1

To find the separation of the slits in a double-slit diffraction pattern, we can use the formula y = m * λ * L / d, where y is the position of the interference maxima, m is the order of the maxima, λ is the wavelength of the light, L is the distance between the double slit and the screen, and d is the separation of the slits. Without knowing the distance L, we cannot determine the exact separation of the slits. However, we can set up the equation using the given information.

Step-by-step explanation:

To find the separation of the slits, we can use the formula for the position of the interference maxima in a double-slit diffraction pattern:

y = m * λ * L / d

where y is the position of the maxima, m is the order of the maxima, λ is the wavelength of the light, L is the distance between the double slit and the screen, and d is the separation of the slits.

In this case, we know that there are nine interference peaks inside the central maximum, so m = 9. We are given the wavelength of the light (589 nm) and the slit width (2.5 μm). The distance between the double slit and the screen is not given, so we cannot calculate the exact separation of the slits.

y = 9 * 589 nm * L / d

In conclusion, without knowing the distance between the double slit and the screen, we cannot determine the exact separation of the slits. However, we can use the given information to set up the equation and solve for the unknown.