Question

the figure below shows the result of a double - slit diffraction experiment with light of wavelength 510 nm. the pattern is closely spaced bright and dark fringes. only the central portion of the pattern is shown. except for the missing spots, the bright spots are separated by a distance of y = 1.61 mm. the pattern is observed on a screen that is 3.91 m from the slits. how far apart are the slits (in mm)?

Explanation:

Step1: Recall double - slit formula

The formula for the position of bright fringes in a double - slit diffraction experiment is $y = \frac{m\lambda L}{d}$, where $y$ is the distance between adjacent bright fringes, $m = 1$ (for adjacent fringes), $\lambda$ is the wavelength of light, $L$ is the distance between the slits and the screen, and $d$ is the distance between the two slits. We need to solve for $d$, so we can re - arrange the formula to $d=\frac{\lambda L}{y}$.

Step2: Convert units

First, convert the wavelength $\lambda$ from nanometers to meters. Given $\lambda = 510\ nm=510\times10^{-9}\ m$. The distance between fringes $y = 1.61\ mm = 1.61\times 10^{-3}\ m$, and the distance to the screen $L = 3.91\ m$.

Step3: Substitute values into the formula

Substitute $\lambda = 510\times 10^{-9}\ m$, $L = 3.91\ m$, and $y = 1.61\times 10^{-3}\ m$ into the formula $d=\frac{\lambda L}{y}$.

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Step4: Convert to millimeters

Since $1\ m = 1000\ mm$, we convert $d$ to millimeters: $d=1.23857\times 10^{-3}\ m\times1000\ mm/m = 1.24\ mm$ (rounded to three significant figures).

Answer:

The distance between the slits is approximately $\boxed{1.24}$ mm.