Degrees of MEng, BEng and BSc in Engineering
Optical Engineering 2 (ENG2088)
Friday 13th May 2022
0930–1100 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.
• This is an open book exam and you may consult your notes and any other available reference material. However, you are advised against directly copying from lecture slides or published materials.
• Marks will be awarded on the basis of understanding and application of the subject. Therefore candidates should ensure their answers show all intermediate steps and as- sumptions in calculations. Answers given without relevant working or justification will receive partial marks only.
• A computational device or calculator may be used.
• 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 thin convex lens has a focal length of 60mm. It is used to image an object placed 40mm in front ofthe lens. There is an aperture of diameter 20mm placed a distance 10mm behind the lens.
(a) Draw a diagram of the optical setup. Draw and label the marginal rays. [8]
(b) Determine the size and position of the entrance and exit pupils. [7]
(c) What is the type and location of the image? [4]
(d) What is the image magnification? [4]
(e) What is the value of the numerical aperture? [5]
Q2. A student compound microscope comes with 3 objectives: 4× (NA=0.1), 10× (NA=0.25) and 40× (NA=0.65), and a 10× eyepiece.
(a) What is the focal length of the 10× objective (assuming the standard tube length of 160mm) [4]
(b) What is the distance in air between the objective lens and the object? [4]
(c) What is the focal length of the 10× eyepiece? Assume a close working distance of 250mm. [4]
lenses could be used for eyesight to resolve an optical image of a red blood cell.
Indicate the assumptions you have used in this determination.
Q3. A Young’s double-slit experiment is carried out using visible monochromatic light to illuminate a pair of narrow slits separated by d = 0.25mm.
(a) If the separation between bright fringes at the centre of the interference pattern is observed to be 7.0mm on a screen a distance of 3.0m from the slits, what is the wavelength of the light?
(b) A perspex wedge (refractive index of 1.50) is placed over the slits as shown in figure Q3. If the wedge angle is 0.045◦ , what happens to the interference pattern on the screen?
Figure Q3: A perspex wedge placed before the double slits (not to scale)
Q4. Light from the sky refiects of the surface of a pond. Use a refractive index of 1.33 for the water.
(a) What should be the orientation of a polariser in order to attenuate refiections from the pond surface?
(b) For what incident angle on the pond surface will the refiected light be observed to vanish?
Q5. A Michelson interferometer uses a laser with a wavelength of 530nm. A cuvette of thickness 10mm is placed in one arm containing a glucose solution. As the glucose concentration increases, 88 fringes are observed to emerge at the screen. What is the change in refractive index of the glucose solution?