Degrees of MEng, BEng and BSc in Engineering
OPTICAL ENGINEERING 2 (ENG2088)
Friday 21st May 2021
Release time: 0930 (BST) for 3 hours
Recommended time for completion: 90 minutes
Total 100 marks.
Answer ALL questions.
• The numbers in square brackets in the right-hand margin indicate the marks allotted to the part of the question against which the mark is shown. These marks are for guidance only.
• A physical or software calculator may be used. Candidates should ensure their answers show all intermediate steps in calculations or otherwise risk a reduction in the awarded marks.
• This is an open book exam and you may consult your notes and any other available reference material. However, the answers you submit must be entirely your own work — the marker needs to be able to assess your understanding of the material. Do not copy from lecture slides, books, online sources or anywhere else.
• Although you can discuss how to approach the exam, and revise with other students, you must not discuss specific exam questions or answers with other students. This is collusion and will result in conduct action.
Q1. A right-angled prism can be used to return an optical ray in the same plane, as shown in [9]
figure Q1. What is the minimum refractive index of the prism for this to occur by total internal reflection?
Figure Q1: Return of an optical ray using a right-angle prism
Q2. A compact camera has the following specifications:
Sensor: “1-inch” CMOS (13.2mm × 8.8mm), 20.1 MP, aspect ratio 3:2
Lens: 24 to 120mm, f /1.8–2.8.
Using the maximum focal length at an aperture setting of f /2.8,
(a) Make a sketch of the optical system, simplifying the camera to a single lens with a [8]
co-located aperture. Draw and label a marginal ray from an object located at infinity.
Draw and label the chief ray taken from the edges of the entrance window.
(b) What is the aperture diameter? [4]
(c) What is the horizontal angular field-of-view? [6]
(d) Calculate the permissible circle of confusion diameter C, typically taken as 1/1500 of the sensor diagonal dimension. How does this compare to the pixel pitch? [4]
(e) Determine the value for the hyperfocal distance [5]
(f) What is the minimum distance that an object would appear in acceptable focus, whilst objects at infinity also appear in acceptable focus? What is the required camera focus setting? [5]
Q3. The refractive index of water for visible light can be taken as n = 1.33.
(a) What is the (irradiance) reflectivity R(θ = 0) for normal incidence from a flat water surface? [5]
(b) What is Brewster’s angle θB in air for a flat water surface? [5]
(c) What is the (irradiance) reflectivity RTE(θB) for transverse-electric linear polarised light at Brewster’s angle for a flat water surface? [9]
Q4. The double slit shown in figure Q4 is illuminated by a laser with a wavelength of 500nm.
(a) Determine the mathematical form. of the Fraunhofer difraction pattern. [6]
(b) How many bright fringes will be displayed within the central lobe? [6]
(c) Sketch the difraction pattern. [6]
(d) A thin transparent plate is introduced immediately in front of one of the slits only. It results in an optical phase diference of π radians. What happens to the fringe pattern? [6]
Figure Q4: Pair of slits in an opaque screen. One major unit on the grid corresponds to a length 0. 1mm
Q5. A green LED emits with a centre wavelength ofλ = 530nm and alinewidth of Δλ = 40nm.
(a) What is the coherence length of this optical source? [6]
(b) This LED with a difuser is used as the optical source for a Michelson interferometer. Describe the visibility of interference fringes as the arm length diference starts at
-1mm and increases monotonically to 1mm. [4]
(c) Calculate an estimate for the total number of visible fringes which appear and then disappear over this scan range. [6]