HardPhysicsHigh School (11–12)OpticsNumericalpython

A student has a single slit that is 0.15 mm wide, cut in a thin metal foil…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A student has a single slit that is $0.15$ mm wide, cut in a thin metal foil. She lights it with an orange lamp of wavelength $600$ nm in air and looks at the pattern on a screen that is $1.20$ m behind the slit. First she measures the width of the central bright band in air. Then she sinks the slit and the screen together in a tank of water of refractive index $1.33$ and measures again. She keeps the lamp and the foil in the same positions the whole time, so only the surroundings of the slit change. She also reads that a beam keeps its width up to a certain distance from a slit, and she wants to know that distance. Find the width of the central maximum in air. Find the new width in water. Find the width of slit that, in water, gives back the width that was seen in air. Find also the Fresnel distance of the original slit in air.

Need a reminder? The key ideaShow

Dark places of a single slit are at $a\sin\theta = n\lambda$ , with $n = \pm1, \pm2, \dots$ For small angles $y = n\lambda D/a$ . The central maximum is $w = 2\lambda D/a$ wide. In a medium the wavelength is $\lambda_0/n$ . The Fresnel distance is $a^2/\lambda$ .

\displaystyle w = \frac{2\lambda D}{a}

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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