Free Response Practice Questions : Optics1. a. Light of a single wavelength is incident on a single slit of width w (w is a few wavelengths.) Sketch a graph of the intensity as a function of position for the pattern formed on a distant screen.

b. Repeat for the case in which there are two slits. The slits are of width w and are separated by a distance d (d >> w). Sketch a graph of the intensity as a function of position for the pattern formed on a distant screen.

2. Light consisting of two wavelengths, a = 4.4 x 10–7 meter and b = 5.5 x 10–7 meter, is incident normally on a barrier with two slits separated by a distance d. The intensity distribution is measured along a plane that is a distance L = 0.85 meter from the slits as shown above. The movable detector contains a photoelectric cell whose position y is measured from the central maximum. The first-order maximum for the longer wavelength b occurs at y = 1.2 x 10–2 meter.

a. Determine the slit separation d.

b. At what position, Ya, does the first-order maximum occur for the shorter wavelength a?

Free Response Practice Questions : Optics

3. An object of height 1 centimeter is placed 6 centimeters to the left of a converging lens whose focal length is 8 centimeters, as shown on the diagram above.

(a) Calculate the position of the image. Is it to the left or right of the lens? Is it real or virtual?

(b) Calculate the size of the image. Is it upright or inverted?

(c) On the diagram, locate the image by ray tracing.

(d) What simple optical instrument uses this sort of object-image relationship?

4. The surface of a glass plate (index of refraction n3 = 1.50) is coated with a transparent thin film (index of refraction n2 = 1.25). A beam of monochromatic light of wavelength 6.0 x 10 –7 meter traveling in air (index of refraction n1 = 1.00) is incident normally on surface S1 as shown. The beam is partially transmitted and partially reflected.

a. Calculate the frequency of the light.

b. Calculate the wavelength of the light in the thin film.

The beam of light in the film is then partially reflected and partially transmitted at surface S2

c. Calculate the minimum thickness d1 of the film such that the resultant intensity of the light reflected back into the air is a minimum.

d. Calculate the minimum nonzero thickness d2 of the film such that the resultant intensity of the light reflected back into the air is a maximum.

Free Response Practice Questions : Optics

Answers1.

2.

a) m λB = d x / L … (1) (5.5x10–7) = d (1.2x10–2) / (0.85) d = 3.9x10–5 m

b) m λa = d x / L … (1) (4.4x10–7) = (3.9x10–5) x / (0.85) x = 9.6x10–3 m

3.

a) 1/f = 1/do + 1/di … 1/8 = 1/6 + 1/di … di = –24 cm, left of lens, virtual

b) M = – di / do … M = – (–24) / 6 = +4 … M = hi / ho … 4 = hi / 1 cm … hi = 4 cm, upright

c)

d) Magnifying glass, or telescope / microscope.

4.

a) c = f λ … 3x108 = f (6x10–7) … f = 5x1014 Hz.

b) n1 λ1 = n2 λ2 … (1) (6x10–7) = (1.25) = 4.8x10–7 m = 480 nm

c) The light is traveling to progressively more dense materials, so undergoes ½ λ phase shifts at both boundaries S1 and S2 essentially canceling out this phase shift (from flips). To get minimum intensity (destructive), the total phase shift from traveling in the film should be ½ λfilm so the film thickness should ¼ λfilm = ¼ 480 nm = 120 nm

d) Based on the same analysis above. To get maximum intensity (constructive) the total phase shift from traveling in the film should be 1 λfilm, so the film thickness should be ½ λfilm = ½ 480 nm = 240 nm