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Light as wave

Light is a wave (an electromagnetic wave)  and  thus  light has a wave length , frequency and  speed.

 

It holds:  

 

 λ = c/f  of  c=f λ

 

c  speed of light in m.s-1                    

f   frequency in Hz

λ  wave length in m                               c en λ depends on the medium

 

Example  

A certain kind of light has in vacuum (air) a wave length of 5.60 x 10-7 m.

Find the frequency

 

c=f λ

3.00 x 108=(5.60 x 10-7) (f)

f = 5.36 x 1014 Hz

 

Diffraction grating

A diffraction grating consists of many narrow, parallel slits equally spaced.

A parallel bundle of rays falls perpendicular  to the grating

In each slit the light bends in every direction.

Behind the grating is interference .

In certain directions the waves interfere constructively. 

This is at a path difference of rays from successive slits  of  0 λ , 1λ , 2 λ , etc

 

Diffraction grating equation:

Diffraction_grating

 

n λ =  d sin αn  

                                                                                  

λ   wavelength

d   grating constant (distance between the slits)

αn  angle of the maxima

n   order maximum   1, 2, 3 …  

 

For  the first order           :  λ  = d sin α1

For  the second order      : 2λ = d sin α2

 

 

 

diffraction_grating_1

 

 

 

 

 

 

 

 

 

 

Example  

diffraction_grating_2

Perpendicular to a grating falls a parallel bundle of rays.                      

 

The grating has 5,000 slits per cm. At a distance of 2.00 m is a screen parallel at the grating.  The distance between the both 2e order maxima is 3.20 m.

 

Calculate the wavelength of the light.

 

d = 1/5000 = 2.00 x 10-4 cm = 2.00 x 10-6 m

 

x2= 1.60 m       tan α2=1.60/2.00 = 0.800   

α2= 38.660 o  

 

sin α2=0.625   

 

2 λ = d sin α2     2 λ =( 2.00 x 10-6) (0.625)       λ= 6.3 x 10-7 m