GOAL Calculate properties of a concave mirror. PROBLEM Assume a certain concave,
ID: 1359513 • Letter: G
Question
GOAL Calculate properties of a concave mirror.
PROBLEM Assume a certain concave, spherical mirror has a focal length of 10.0 cm. Determine whether the image is real or virtual, inverted or upright, and larger or smaller. (a) Locate the image and find the magnification for an object distance of 25.0 cm. Do the same for object distances of (b) 10.0 cm and (c) 5.00 cm.
STRATEGY For each part, substitute into the mirror and magnification equations. Part (b) involves a limiting process because the answers are infinite.
SOLUTION
(A) Find the image position for an object distance of 25.0 cm. Calculate the magnification and describe the image.
Use the mirror equation to find the image distance.
Substitute and solve for q. Note that pand f are positive.
q = 16.7 cm
Because q is positive, the image is in front of the mirror and is real. The magnification is given by substituting into equation.
The image is smaller than the object because |M| < 1, and it is inverted because M is negative.
(B) Locate the image distance when the object distance is 10.0 cm. Calculate the magnification and describe the image.
The object is at the focal point. Substitute p = 10.0 cm and f = 10.0 cm into the mirror equation.
Because M = -q/p, the magnification is also infinite.
(C) Locate the image distance when the object distance is 5.00 cm. Calculate the magnification and describe the image.
Once again, substitute into the mirror equation.
q = -10.0 cm
The image is virtual (behind the mirror) because q is negative. Calculate the magnification.
The image is larger (magnified by a factor of 2) because |M| > 1, and upright because M is positive.
LEARN MORE
REMARKS Note the characteristics of an image formed by a concave, spherical mirror. When the object is outside the focal point, the image is inverted and real; at the focal point, the image is formed at infinity; inside the focal point, the image is upright and virtual.
QUESTION What location does the image approach as the object gets arbitrarily far away from the mirror? (Select all that apply.)
The focal point.Half the radius of the mirror.Infinity.The mirror itself.The radius of curvature of the mirror.
PRACTICE IT
Use the worked example above to help you solve this problem. Assume that a certain concave spherical mirror has a focal length of 12.0 cm.(a) Locate the image and find the magnification for an object distance of 30.0 cm. (If the image location or magnification is infinite, type INFINITY.)
(b) Do the same for an object distance of 12.0 cm
(c) Do the same for an object distance of 6.00 cm.
EXERCISEHINTS: GETTING STARTED | I'M STUCK!
Use the values from PRACTICE IT to help you work this exercise. If the object distance is 24.0 cm, find the image distance and the magnification of the mirror.
1 + 1 = 1 p q fExplanation / Answer
QUESTION What location does the image approach as the object gets arbitrarily far away from the mirror? (Select all that apply.)
The focal point.
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A) p = 30 cm
f = 12 cm
q = ?
1/30 + 1/q = 1/12
1/q = 1/12 - 1/30
q = 20 cm
M = -q/p = -20/30= -0.667
B) 1/12 + 1/q = 1/12
1/q = 0
q is INFINITY
M = INFINITY
C) 1/6 + 1/q = 1/12
1/q = 1/12 - 1/6 =
q = -12 cm
M = 12/6 = 2
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p = 24 cm
f = 12 cm
1/q = 1/12 - 1/24 =
q = 24 cm
M = -q/p= -24/24 = 1
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