3. (6 pts) Consider the design of a Fabry-Perot interference filter consisting o

Question

3. (6 pts) Consider the design of a Fabry-Perot interference filter consisting of two sapphire plates, each 1 mm in thickness, two thin Ag layers comparable to that shown in the reflectance curve above, and a LaSFN9 glass dielectric layer. a. (3 pts) How thick (in m) should this dielectric layer be in order to transmit 514.5 nm in the first order for light incident along the filter normal? b. (3 pts)Estimate the overall transmittance of this filter at its peak throughput of 514.5 nm? (NOTE: Transmittance data provided for sapphire includes losses from reflection; assume transmittance is independent of thickness.) LaSFN9 Glass 100 100 90 70 70 501 20 20 10 10 00 200 300 500 00 2000 3000 S000 8OG 800 1200 1600 2000 WAVELENGTH IN NANOMETERS External transmittance for 1-mm-thick uncoated sapphire External transmission for 10-mm-thick LaSFN9 glass

Explanation / Answer

(a) To find the thickness of the dielectric layer, d , therefore, for the first order n = 1 since the incidence is normal, therefore, applying bragg's law we get,

nL = 2d sinQ , where L is the wavelength lambda and Q is the angle of incidence of the light on the dielectric layer, since Q = 900 , we get

nL = 2d

L = 2 x 514.5 nm = 1029 nm = 1029 x 10-9 m.

(b) The overall transmission of the filter at it's peak will be given by, since the transmittiance does not depend on the thickness, therefore,

T = e-L = e-514.5 = 3.59 x 10-224.  

  

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.