2693:
The focal length of a lens is inversely proportional to the quantity
(
n
),
1
where
n
is the
index of refraction of the lens material. The value of
n
, however, depends on the
wavelength of the light that passes through the lens. For example, one type of flint glass
has an index of refraction of
for red light and
n
n
r
1572
.
v
1605
.
in violet light. Now,
suppose a white object is placed 24.00 cm in front of a lens made from this type of glass.
If the red light reflected from this object produces a sharp image 55.00 cm from the lens,
where will the violet image be found?
Picture the Problem
: The figure shows an object 24.00 cm
in front of a lens, for which the focal length is dependent on
the wavelength of light. This results in different image
distances for the red and violet light.
Strategy:
Calculate the focal length for the red light using
equation 2616 and the given data. Because the focal lengths
are inversely proportional to (
n
−
1), use the ratio
v
r
r
v
1
f
f
n
n
1
to calculate the focal length for
violet light. Finally, use equation 2616 to calculate the
image distance.
Solution:
1.
Calculate the
focal length for red light:
1
1
r
o
i,r
1
1
1
1
16.709 cm
24.00 cm
55.00 cm
f
d
d
2.
Calculate the focal length
of the violet light:
r
v
r
v
1
1.572
1
16.709 cm
15.80 cm
1
1.605
1
n
f
f
n
3.
Calculate the violet image distance:
1
1
i,v
v
o
1
1
1
1
46.2 cm
15.80 cm
24.00 cm
d
f
d
Insight:
The violet light is in focus 8.8 cm before the red light. This blurring of the colors in an image is called
chromatic aberration
.
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 Fall '06
 Alexandrakis
 Physics, Light

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