Physics 1C
Week 6 Questions
Fall 1998
1. A bubble of CO2 is submerged in a glass of beer and slowly floating up to the surface. The bubble makes a
tiny lens. If you judge by its shape, what kind of lens is it? Does it make a parallel light converge or
diverge?
2. You are marooned on a desert island and want to use your eyeglasses to start a fire. Can this be done if you
are farsighted? If you are nearsighted? Explain.
3. A woman who has been wearing -2.50 D glasses for many years notices that her vision is changing. Her far
point has moved 20% inward from its former value. Calculate the power of the new lenses she needs to
correct her vision.
4. Suppose we have two lenses with focal lengths of 2.0 cm and 2.0 mm. How should they be arranged to
make a microscope to view, with a relaxed eye, an object 2.5 mm from the front lens? What is the
separation between lenses? What is the magnification of the device?
5. What is the polarization angle for reflection of light from the surface of a piece of glass (ng = 1.55)
immersed in water (nw = 1.33)? In which direction is the light polarized?
6. A collimated beam of light ( = 550 nm) falls on a screen containing a pair of long, narrow slits separated
by 0.10 mm. Determine the separation between the two third-order maxima on a screen 2.00 m from the
apertures.
Physics 1C
Week 6 Solutions
Fall 1998
1. Bubble is a positive lens (from its shape, both surfaces are convex). It diverges parallel light.
2. Farsighted people have positive lenses (eyes too weak). Positive lens can make real image of sun and start
fire. This type of lens is thicker in the center. Nearsighted people use negative lenses (thinner in the
center). Negative lenses diverge light and cannot make a real image of the sun (i.e. can't start a fire). How
about using the concave surface facing the eye as a mirror? You can make a real image that way, but there
won't be much energy in the image, and it probably won't start a fire (although worth a try).
farsighted person
positive eyeglass lens
fatter in the center
nearsighted person
negative eyeglass lens
thinner in the center
3. If power = -2.50 diopters, then the focal length is -0.4m = -40cm. An object at infinity will need to have its
image be no further from the eye than the far point. Since 1/s + 1/s' = 1/f, with s = infinity, this means the
far point should be equal to f (ignoring the separation between the eyes and the eyeglass lenses). So the far
point was originally at 40 cm, and is now diminished to 32 cm. The new lenses should have a focal length
equal to this, so that the power is -3.13 D.
4. The shorter focal-length lens is the objective for which 1/(0.0025 m) + 1/si = 1/(0.0020 m), si = 0.010 m; the
lens separation is si + fE = 0.010 m + 0.020 m = 0.030m. MAO = -(si - fO)/fO = -4  , while MAE = (0.254
m)(50 D) = 12.7  , and the product of these MA = -51  .
eye
f1 = 2 mm
f1 = 2 mm
f2 = 2 cm
f2
O1 = 2.50 mm
i1 = O2
(inverted virtual image at i2 =  )
5. tan p = nt/ni = 1.55/1.33, p = 49.4o. The direction is parallel to the interface and perpendicular to the
reflected light ray.
6. y3 = 3(2.00 m)(550  10-9 m)/(0.10  10-3 m) = 0.033 m and the separation is twice this, or 66 mm.