1) Watch Glass Experiment A watch glass is held at arm’s length and a viewer see
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Question
1) Watch Glass Experiment
A watch glass is held at arm’s length and a viewer sees an image formed by the concave surface. The radius of curvature the surface is similar to that of a basketball. According to Wikipedia, the circumference of a basketball is approximately 75 cm. Assume that the viewer holds the watch glass 0.7 m from her face. That is, the object distance is 0.7 m.
(a) Find the focal length of the watch glass. Make a neat ray diagram to scale and note whether the image is real, virtual, upright, or inverted. Estimate the object distance and the magnification. The scale drawing can be made on this grid or on a separate piece of graph paper.
(b) Using the same focal length and object distance as above, use the algebraic approach to solve for the image distance and magnification exactly.
2) Image Magnification in Woman at Her Toilette
In our physics tour of the Worcester Art Museum, we look at the painting Woman at Her Toilette, which contains a small mirror with an image of a woman’s face. In the tour guide, it is claimed that the magnification has value 1/3 when the object distance is equal to the radius of curvature of a convex mirror. In this problem we will confirm this algebraically. Show that m = + 1/3 when the object distance is equal to the radius of curvature, for a convex mirror.
Explanation / Answer
f = focal length = - R/2
do = object distance = R
di = image distance
using the mirror equation
1/f = 1/di + 1/do
1/(- R/2) = 1/di + 1/R
-2/R - 1/R = 1/di
di = - R/3
magnification is given as
m = - di/do = - (-R/3) / R = 1/3
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