King Saud University  College of Applied Medical Sciences Optometry Department  OPTO-356: Second Mid-Term Exam Nov. 12th, 2003

 

                         Time Allowed:                     Two Hours

                             Student’s Name:                 

                             Student’s Number:               

                            Course Instructor:               Dr. Idriss M. Bedja

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THEORY:

QUESTION 1:

List the main differences between the laser source and incandescent lamp source.

            Laser source                                  Incandescent lamp source

Stimulated emission                |    Spontaneous emission

Coherent light                         |    Incoherent light

Monochromatic, and confined |    Multi-wavelnegths and

parallel Beam                          |    divergent beam

 

QUESTION 2:

a) Why can laser be safely used for medical surgery?  Because specific laser wavelength is being absorbed by a specific type of biological tissue.

 

b) Describe briefly one example of medical application:  In Glaucoma we have high fluid pressure which may destroy the optic nerve. Use a laser to open a tiny hole to retrieve a destructive pressure .

 PROBLEM 1:

Measurements are made of the intensity distribution in a Young’s interference pattern.  At a particular value of y (distance from the center of the screen), it is found that I/I₀ = 82% when light of wavelength 5890 A is used. 

a)     A)  What wavelength of light should be used in order to reduce the relative intensity at the same location to 55%?

b)     B)  What is the shift (variation) in minimum phase differences in radians between sources accompanied with this change in wavelengths?

c)       What is the new deviation angle θ attributed to the new wavelength?

Solution:

Data:                                       Requests:

Iav/Io = 0.82                           l₂=  ? (if new Iav/Io = 0.55) at same y

l₁=  5890 A°                           DF = F(l₂) - F(l₁) = ?

                                                q (l₂) = ?

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a)-  Same location y, also same  |πδ/l₂= cos-1(0.742) = 42.1°

Path difference δ, for both          |           l₂= 351.1 nm

 equations.                                   |          

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Iav/Io = cos² (πδ/l₂) = 0.55      |           b)- DF = F(l₂) - F(l₁) = ?

We need so to get δ, from           |           F(l₁)/2=  πδ/l₁ ----- F(l₁)= Iav/Io = 0.82                               |          50.2°

0.82 =  cos² (πδ/l₁)                   | F(l₂)/2=  πδ/l₂ ----- F(l₂)= 84.2°

cos (πδ/l₁) = Ö0.82 = 0.91        |

πδ/l₁= cos-1 (0.91) = 25.1 °    |           DF = 84.2° - 50.2° = 34°

δ = 25.1 °x l₁    = 82.13 nm                  

         180°

cos (πδ/l₂) = Ö0.55                                    

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PROBLEM 2:

A soap bubble of index of refraction 1.33 reflects both red and green colors in white light.  What minimum thickness of soap bubble will allow this to happen? (In air, λ_red =700 nm, λ_green=500 nm.)

Solution:         n=1.33                        t_min= ?                                               

l_r=700 nm 

l_g=500 nm

The system is air /layer/air ------ low index/high index/ low index ---so we use formula of constructive interference   

2t=(m + ½)/l/n

 

       For Red                                  |                       For Green

                                                                                                    

t=(m + ½)/l/2n                                         |                       t=(m + ½)/l/2n

m=0  t= 131.6 nm                        |     m=0    t= 94 nm                 

m=1   t= 394.7 nm                                      |      m=1    t= 282 nm

m=2   t= 657.2 nm                        |    m=2    t= 470 nm               

                                                                     |    m=3    t= 658 nm

                                                                                                 

So min thikness which allow both colors is                

                             t= 657.2 nm