Question

In your summer job at an optics company, you are asked to measure the wavelength $\lambda$ of the light that is produced by a laser. To do so, you pass the laser light through two narrow slits that are separated by a distance $d$. You observe the interference pattern on a screen that is $0.900 \mathrm{~m}$ from the slits and measure the separation $\Delta y$ between adjacent bright fringes in the portion of the pattern that is near the center of the screen. Using a microscope, you measure $d$. But both $\Delta y$ and $d$ are small and difficult to measure accurately, so you repeat the measurements for several pairs of slits, each with a different value of $d$. Your results are shown in Fig. $\mathbf{P} 35.50,$ where you have plotted $\Delta y$ versus $1 / d .$ The line in the graph is the best-fit straight line for the data. (a) Explain why the data points plotted this way fall close to a straight line. (b) Use Fig. $\mathrm{P} 35.50$ to calculate $\lambda$.

          In your summer job at an optics company, you are asked to measure the wavelength $\lambda$ of the light that is produced by a laser. To do so, you pass the laser light through two narrow slits that are separated by a distance $d$. You observe the interference pattern on a screen that is $0.900 \mathrm{~m}$ from the slits and measure the separation $\Delta y$ between adjacent bright fringes in the portion of the pattern that is near the center of the screen. Using a microscope, you measure $d$. But both $\Delta y$ and $d$ are small and difficult to measure accurately, so you repeat the measurements for several pairs of slits, each with a different value of $d$. Your results are shown in Fig. $\mathbf{P} 35.50,$ where you have plotted $\Delta y$ versus $1 / d .$ The line in the graph is the best-fit straight line for the data. (a) Explain why the data points plotted this way fall close to a straight line. (b) Use Fig. $\mathrm{P} 35.50$ to calculate $\lambda$.

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