Monochromatic light of wavelength 633 nm falls on a slit. If the angle between the first bright fringes on either side of the central maximum is 32°, estimate the slit width.

(a) For a given wavelength λ, what is the minimum slit width for which there will be no diffraction minimum? (b) What is the minimum slit width so that no visible light exhibits a diffraction minimum?

A single slit 0.10 mm wide is illuminated by 450-nm light. What is the width of the central maximum in the diffraction pattern on a screen 5.0 m away?

If you double the width of a single slit, the intensity of the light passing through the slit is doubled. (a) Show, however, that the intensity at the center of the screen increases by a factor of 4. (b) Explain why this does not violate conservation of energy.

A slit of width D = 22 μm is cut through a thin aluminum plate. Light with wavelength λ = 620nm passes through this slit and forms a single-slit diffraction pattern on a screen a distance ℓ = 2.0 m away. Defining x to be the distance between the two first minima on either side of the center in this diffraction pattern ( m = +1 and m = -1), find the change ∆x in this distance when the temperature T of the metal plate is changed by an amount ∆T = 55 C°. [Hint: Since λ ≪ D, the first minima occur at a small angle.]

Pellets of mass 2.0 g are fired in parallel paths with speeds of 150 m/s through a hole 3.0 mm in diameter. How far from the hole must you be to detect a 1.0-cm-diameter spread in the beam of pellets?

Explain why the secondary maxima in the single-slit diffraction pattern do not occur precisely at β/2 = (m + 1/2)π where m = 1, 2, 3, ... Carefully and precisely plot the curves y = β/2 and y = tan β/2. From their intersections, determine the values of β for the first and second secondary maxima. What is the percent difference from β/2 = (m + 1/2)π?

A 20x telescope has a 12-cm-diameter objective lens. What minimum diameter must the eyepiece lens have to collect all the light rays from an on-axis distant source?