The electrons in a cathode-ray tube are accelerated through a 250 V potential difference and then shot through a 33-nm-diameter circular aperture. What is the diameter of the bright spot on an electron detector 1.5 m behind the aperture?

Monochromatic light falls on a slit that is 2.60 x 10⁻³ mm wide. If the angle between the first dark fringes on either side of the central maximum is 29.0° (dark fringe to dark fringe), what is the wavelength of the light used?

Light of wavelength 580 nm falls on a slit that is 3.50 x 10⁻³ mm wide. Estimate how far the first brightest diffraction fringe is from the strong central maximum if the screen is 10.0 m away.

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 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) 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, ... .

(b) By differentiating Eq. 35–7 with respect to β show that the secondary maxima occur when β/2 satisfies the relation tan(β/2) = β/2.

(c) 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 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.]