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For what ratio of slit width to wavelength will the first minima of a single- slit diffraction pattern occur at \(\pm 90^{\circ} ?\)

Light with wavelength \(633 \mathrm{nm}\) is incident on a \(2.50-\mu \mathrm{m}\) -wide slit. Find the angular width of the central peak in the diffraction pattern, taken as the angular separation between the first minima.

Find the intensity as a fraction of the central peak intensity for the second secondary maximum in single-slit diffraction, assuming the peak lies midway between the second and third minima.

Find the minimum angular separation resolvable with \(633-\mathrm{nm}\) laser light passing through a circular aperture of diameter \(2.1 \mathrm{cm} .\)

Find the minimum telescope aperture that could resolve an object with angular diameter 0.35 arcsecond, observed at 520 -nm wavelength. (Note: 1 arcsec \(=1 / 3600^{\circ}\) )

What's the longest wavelength of light you could use to resolve a structure with angular diameter 0.44 mrad, using a microscope with a 1.2 -mm-diameter objective lens?

In bright light, the human eye's pupil diameter is about \(2 \mathrm{mm}\). If diffraction were the limiting factor, what's the eye's minimum angular resolution under these conditions, assuming \(550-\mathrm{nm}\) light?

Find the angular position of the second-order bright fringe in a double-slit system whose slit spacing is \(1.5 \mu \mathrm{m}\) for (a) red light at \(640 \mathrm{nm},\) (b) yellow light at \(580 \mathrm{nm},\) and (c) violet light at \(410 \mathrm{nm}\).

A double-slit experiment has slit spacing \(0.035 \mathrm{mm},\) slit-toscreen distance \(1.5 \mathrm{m},\) and wavelength \(490 \mathrm{nm} .\) What's the phase difference between two waves arriving at a point \(0.56 \mathrm{cm}\) from the center line of the screen?

For a double-slit system with slit spacing \(0.0525 \mathrm{mm}\) and wavelength \(633 \mathrm{nm},\) at what angular position is the path difference a quarter wavelength?