(a) How far away can a human eye distinguish two car headlights 2.0 m apart? Consider only diffraction effects and assume an eye pupil diameter of 6.0 mm and a wavelength of 560 nm. (b) What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? In reality, it is about of arc. Why is it not equal to your answer in (b)?

(a) Derive an expression for the intensity in the interference pattern for three equally spaced slits. Express in terms of δ = 2πd sin θ / λ where d is the distance between adjacent slits and assume the slit width D ≈ λ.

(b) Show that there is only one secondary maximum between principal peaks.

Suppose the angles measured in Problem 42 were produced when the spectrometer (but not the source) was submerged in water. What then would be the wavelengths (in air)?

Red laser light from a He–Ne laser (λ = 632.8 nm) creates a second-order fringe at 53.2° after passing through a grating. What is the wavelength λ of light that creates a first-order fringe at 21.2°?

The wings of a certain beetle have a series of parallel lines across them. When normally incident 520-nm light is reflected from the wing, the wing appears bright when viewed at an angle of 56°. How far apart are the lines?

A beam of 125-eV electrons is scattered from a crystal, as in X-ray diffraction, and a first-order peak is observed at θ = 43°. What is the spacing between planes in the diffracting crystal? (See Section 35–11.)

What is the highest spectral order that can be seen if a grating with 6800 slits per cm is illuminated with 633-nm laser light? Assume normal incidence.

A laser beam of wavelength λ = 632.8 nm shines at normal incidence on the reflective side of a compact disc. (a) The tracks of tiny pits in which information is coded onto the CD are 1.60 μm apart. For what angles of reflection (measured from the normal) will the intensity of light be maximum? (b) On a DVD, the tracks are only 0.740 μm apart. Repeat the calculation of part (a) for the DVD.

(III) Derive an expression for the intensity in the interference pattern for three equally spaced slits. Express in terms of δ = 2πd sin θ / λ where d is the distance between adjacent slits and assume the slit width D ≈ λ . Show that there is only one secondary maximum between principal peaks.