24.06 A convex spherical mirror has a radius of curvature of 11.0 cm. A. Calcula
ID: 2100975 • Letter: 2
Question
24.06 A convex spherical mirror has a radius of curvature of 11.0 cm.
A. Calculate the location of the image formed by an 8.00-mm-tall object whose distance from the mirror is 18.0 cm
B. Calculate the location of the image formed by an 8.00-mm-tall object whose distance from the mirror is 10.0 cm .
C. Calculate the location of the image formed by an 8.00-mm-tall object whose distance from the mirror is 2.50 cm .
D. Calculate the location of the image formed by an 8.00-mm-tall object whose distance from the mirror is 9.60 m
Explanation / Answer
As the mirror is convex the focal length is negative
f = R/2 = 11.cm / 2 = -5.5 cm
a)
The object distance, image distance and focal length are related by
1/f = 1/s+1/s'
1/s' = 1/f-1/s
1/s' = s-f/fs
s' = fs/s-f
= (-5.5cm)(18.0cm) / 18cm + 5.5cm
= - 4.21 cm
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b)
s' = fs/s-f
= (-5.5cm)(10.0cm) / 10cm + 5.5cm
= -3.55 cm
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c)
s' = fs/s-f
= (-5.5cm) (2.50cm) / 2.5cm + 5.5cm
= -1.72 cm
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c)
s' = fs/s-f
= (-5.5cm) (960cm) / 960cm + 5.5cm
= -5.47 cm
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