Download 76165s optiikka

766349A WAVE MOTION AND OPTICS
Exercise 9
spring term 2017, week 16
problems 1-3 due on Friday 21.4.
problems 4-6 due on Wednesday 26.4.
1. The sun subtends an angle of 0.5 at the earth's surface, where the irradiance is about
1000 W/m2 at normal incidence.
What is the irradiance of an image
of the sun formed by a lens with
diameter 5 cm and focal length 50
cm?
2. The objective lens of a microscope has a focal length of 16.0 mm and that of the eyepiece is
25.0 mm. The separation of lenses is 221 mm. The final image is viewed at infinity (at far
point).
a) Find the optical length and the magnification of the device.
b) How far from the objective lens the object is situated.
c) A nearsighted person with far point at 50 cm in front of the eye starts to use the microscope.
How much the object distance must be changed and what is the new magnification when the
final image is at the users far point. Assume that the near point is at 25 cm.
3. A small astronomical telescope has objective lens with focal length of 60 cm and diameter of
3.0 cm. The diameter of exit pupil is 2.0 cm. Find the angular magnification.
4. Two waves having parallel electric fields are described by
E1  E01 sin(1  t ) and E2  E02 sin( 2  t ) .
The waves intersect at point P. Find the superposition in case the waves
a) have zero phase difference,
b) have phase difference  .
5. Find the superposition of waves E1  7sin( / 3   t ) and E2  12cos( / 4   t ) .
6. By finding appropriate expressions for k  r , write equations describing a sinusoidal plane wave
in three dimensions, displaying wavelength and velocity, if propagation is
a) along the +z-axis;
b) along the line y  x , z  0 ;
c) perpendicular to the planes x  y  z  constant .