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PHYS2125: OPTICS & RADIATION PHYSICS

 

THIRD OPTICS ASSIGNMENT, 2016

 

Due Date: Tuesday 24 May, 5:00 pm

 

Submit as a .pdf file through the Assignments submission facility in Blackboard.

 

Check after submitting that the file is complete.

 

Name your file <FamilyName>OA3.pdf (e.g., GibsonOA3.pdf)

 

Problems on Material Optics

 

(Maximum marks are shown in brackets)

 

1.

 


 

A common way of specifying the refractive index properties of glass used for optical

 

components is in terms of two numbers, a refractive index and a dispersion index.

 

Refractive indexes are measured at certain standard wavelengths, corresponding to

 

strong spectral line emissions from gases such as hydrogen, helium, cadmium and

 

mercury. The three most commonly used wavelengths are:

 

Designation

 

C

 

d

 

F

 


 

Wavelength (nm)

 

656.3

 

587.6

 

486.1

 


 

The refractive indexes at these wavelengths are designated nC, nd and nF respectively.

 

Dispersion is specified in terms of the Abbe value vd, defined by

 

n 1

 

vd d

 

n F nC

 

A very common type of glass is BK7, which has nd = 1.51680 and vd = 64.17

 

From this information, calculate an approximate value for the group refractive index

 

ng of BK7 at 588 nm.

 

[10]

 


 

2.

 


 

What is the imaginary part of the index of refraction for a medium in which the

 

electric field amplitude of a 488 nm light beam is attenuated to 0.20 of its starting

 

value after travelling a distance of 50 nm in the medium? (Note that when the

 

wavelength of a light beam is quoted, it is always the wavelength in air unless

 

otherwise stated).

 

[6]

 


 

3.

 


 

Under what conditions would the reflectance R and the transmittance T be equal to

 

each other at normal incidence at an interface? What would be the value of R and T

 

under these conditions?

 

[8]

 


 

1

 


 

4.

 


 

For a material in thermal equilibrium at room temperature, T = 300 K, what is the ratio

 

of the upper to lower population density in a pair of states separated by an energy

 

difference corresponding to a wavelength of 633 nm?

 

[6]

 


 

5.

 


 

(i) Calculate the values of the Einstein A and B coefficients for the case of a transition

 

at = 1.15 m with a lifetime of 120 ns (neon gas has a transition like this).

 

(ii) How large would the spectral radiant energy density at this wavelength have to be

 

to make the rate of stimulated emission be equal to the rate of spontaneous emission?

 

(iii) Suppose the radiant energy is supplied in the form of a parallel beam of light with

 

a cross-sectional area of 1.0 mm2. How much power would this beam have within a

 

spectral interval of 0.10 nm?

 

[20]

 


 

bg 13/5/16

 


 

2

 


 

 

Paper#9256884 | Written in 27-Jul-2016

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