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Answer :
Final answer:
The location of the image for the given object distances are 13.6 cm, 20.4 cm, and 40.8 cm. The image is real for an object distance of 39.4 cm, at infinity for an object distance of 20.4 cm, and virtual for an object distance of 10.2 cm. The image is upright for all object distances. The magnification is -0.345 for an object distance of 39.4 cm, -1 for an object distance of 20.4 cm, and -4 for an object distance of 10.2 cm.
Explanation:
To find the location of the image for the given object distances, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
f is the focal length of the mirror
v is the image distance
u is the object distance
For each object distance, we can substitute the given values into the formula and solve for the image distance:
For an object distance of 39.4 cm:
1/f = 1/v - 1/u
1/20.4 = 1/v - 1/39.4
Solving for v, we find that the image distance is 13.6 cm.
For an object distance of 20.4 cm:
1/f = 1/v - 1/u
1/20.4 = 1/v - 1/20.4
Solving for v, we find that the image distance is 20.4 cm.
For an object distance of 10.2 cm:
1/f = 1/v - 1/u
1/20.4 = 1/v - 1/10.2
Solving for v, we find that the image distance is 40.8 cm.
To determine if the image is real or virtual, we can use the sign convention:
If the image distance is positive, the image is real.
If the image distance is negative, the image is virtual.
Using this convention, we can determine the nature of the image for each object distance:
For an object distance of 39.4 cm, the image distance is positive, so the image is real.
For an object distance of 20.4 cm, the image distance is zero, so the image is at infinity.
For an object distance of 10.2 cm, the image distance is negative, so the image is virtual.
To determine if the image is upright or inverted, we can use the magnification formula:
m = -v/u
Where:
m is the magnification
v is the image distance
u is the object distance
For each object distance, we can substitute the given values into the formula and solve for the magnification:
For an object distance of 39.4 cm:
m = -v/u
m = -13.6/39.4
Solving for m, we find that the magnification is -0.345.
For an object distance of 20.4 cm:
m = -v/u
m = -20.4/20.4
Solving for m, we find that the magnification is -1.
For an object distance of 10.2 cm:
m = -v/u
m = -40.8/10.2
Solving for m, we find that the magnification is -4.
Learn more about properties of concave spherical mirrors here:
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Rewritten by : Jeany
