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Trigonometry for Physicists
d sin   n
Machine vision systems
Multiple imaging
Beam where
for a diffraction grating
 Metrology
d = the distance between the lines
of the grating
Fig 1
n = order of beam (small whole number)
= the wavelength of light emerging from the grating
= angle of the beam from the grating
1a) If d = 5 x 10-6 m;
n = 1;  = 6.8o , what is the wavelength of the light (  )?
b) Calculate the wavelength of light that produces a second order ( n = 2) beam at 40o with a diffraction
grating with grating element 2 x 10-6 m.
c) For a diffraction grating if light of wavelength (  ) = 500 nm is to fit the equation
x 10-5 m and n = 2 what must be the value of  ?
d sin   n when d is 4
2) A diffraction grating has a spacing of 1.6 x 10-6 m. A beam of light is incident normally on the grating. The
first order maximum makes an angle of 20o with the undeviated beam. What is the wavelength of the
incident light?
(OCR 2000)
When light enters a glass surface as in Fig 2 it is refracted. This means that the light changes direction.
WorkFGDT 
The ratio of
sin i
is a constant called the Refractive Index and for a boundary between ordinary glass and
sin r
air (going from air into glass) its value is 1.5.
3a) Calculate the angle of incidence (i) needed to give an angle of refraction of 20o if the refractive index is
i.e. Refractive Index =
sin i
. What is i if r = 20o and the Refractive Index = 1.5?
sin r
b) If light arrives at an angle of 15o to the normal at an air-to-glass boundary for which the refractive index is
1.5, what is the expected angle of refraction?
4) The Refractive Index for an air-to-diamond boundary is about 2.42. If light arrives at an angle of 60o to the
normal at an air-to-diamond boundary, what is the expected angle of refraction?
Research: What do you think happens going from glass to air? What formula might be
involved? What does it mean by total internal reflection and how could you work out the
critical angle for glass that would cause it?
WorkFGDT 