mid-term 2008 - ELEC308 Engineering Optics MID-TERM...

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ELEC308 Engineering Optics MID-TERM EXAMINATION DATE: March 28, 2008 TIME: 6:30 am – 9:00 pm PLEDGE OF HONOR On my honor as a student of Hong Kong University of Science and Technology, I have neither received aid from others nor given aid to others while taking this exam. All of the answers represent my own work. Signature: __________________ Date: ________________ Student Name: Student Number:
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Total points: 35 pts. (30 pts. + 5 bonus pts). All the useful equations are in Appendix. 1. (7 pts.) Precise measurement of refractive index of optical material. A prism is made of an optical material with unknown refractive index as shown in figure below. After a monochromatic light ray go through the prism, it is deviated and the deviation angle is δ . The deviation of the light ray by the prism is a function of incident angle, θ i 1 . Prove that when δ reaches to the smallest value, δ m , known as the minimal deviation, the refractive index of the optical material can be measured as ( ) [ ] 2 / sin 2 / sin α α δ + = m n . (This equation forms the basis of one of the most accurate techniques for determining the refractive index of an optical material.) Hint: when δ is smallest, 0 1 = i d d θ δ and ( ) ( ) 2 2 1 1 i t t i θ θ θ θ
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