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?

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.]

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?

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?

(II) A lens appears greenish yellow (λ = 570nm is strongest) when white light reflects from it. What minimum thickness of coating (n = 1.25) do you think is used on such a glass lens (n = 1.56), and why?

A thin oil slick (n_o = 1.50) floats on water (n_w = 1.33). When a beam of white light strikes this film at normal incidence from air, the only enhanced reflected colors are red (653 nm) and violet (392 nm). From this information, deduce the (minimum) thickness t of the oil slick.

Light of wavelength 5.0 x 10⁻⁷ passes through two parallel slits and falls on a screen 5.0 m away. Adjacent bright bands of the interference pattern are 2.0 cm apart.

(a) Find the distance between the slits.

(b) The same two slits are next illuminated by light of a different wavelength, and the fifth minimum for this light occurs at the same point on the screen as the fourth minimum for the previous light. What is the wavelength of the second source of light?