Homework 5 Solutions

HW 5 S12 solns
HW 3_F11
1. Design a little dentist mirror to be fixed at the end of a shaft for use in the mouth. The requirements
are (i) the image seen by the dentist must be erect and (ii) when the mirror is held 1.5 cm from a tooth
the mirror produces an image twice life-size. Draw a simple sketch showing the key locations and mirror
geometry with labels.
1. Make a sketch roughly locating the aperture stop and entrance and exit pupils for the lens
combination shown below. Assume the object point is beyond (to the left of) Fo1.
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2. An optical system, centered on an optical axis, consists of (left to right)
1) Source plane.
2) Thin lens L1 at 40 cm from the source plane.
3) Aperture A at 20 cm farther from L1.
4) Thin lens L2 at 10 cm farther from A.
5) Image plane.
Lens L1 has a focal length of 40/3 cm and a diameter of 2 cm; lens L2 has a focal length of 20/3 cm and a
diameter of 2 cm; aperture A has a centered circular opening of 0.5 cm diameter.
Note: it will be difficult to ray trace to answer the questions below (scale of lenses and distances makes it
hard). You will need to use equations and get real numbers for things to compare. You’ll need to calculate
image locations and magnifications.
(a) Sketch the system.
(b) Find the location of the image plane (as a number).
(c) Locate the aperture stop and entrance pupil (give specific info about location and size).
(d) Locate the exit pupil (give specific info about location and size).
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3. Consider the unaccommodated crystalline lens of the eye as an isolated unit having radii of curvature and a
refractive index as given in Table 19-2 in your textbook (refer to figure 19.3).
(a) Calculate its focal length as a thin lens in air.
(b) Calculate its focal length as a thin lens in its actual environment (see figure 19.3)
(c) Calculate where an incoming ray, parallel to the optical axis, will cross the optical axis. Report this distance
from the back vertex of the lens. Treat the lens as a thick lens of thickness 3.6 mm, in its actual environment.
Include the transmission of the ray through the cornea also (so the ray is parallel to the optical axis in air, before
it hits the cornea).
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(c) Need to use equations for single refracting surface, one at a time. The cornea first finding s1'), then
the refraction at the first lens surface (finding s2'), the refraction at the second lens surface (finding s3').
The final s3' will be the final image formation (with initial object at infinity in front of eye), as measured
from the back vertex of the lens, which is the vertex of the third refracting surface in the calculation.
Graduate Student Problem (PHYS 5271, MEGR 7090 and MEGR 8090)
4. The figure below shows a lens system, an object, and the appropriate pupils. Sketch marginal rays and
the chief ray to locate the image.
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