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An object 2 cm tall is placed 10 cm in front of a concave mirror with a focal length of 5 cm. What is the size of the image?
- a)4 cm
- b)-4 cm
- c)-2 cm
- d)2 cm
Correct answer is option 'C'. Can you explain this answer?
?
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An object 2 cm tall is placed 10 cm in front of a concave mirror with ...
Concave Mirror Basics
Concave mirrors converge light rays, and their properties can be analyzed using the mirror formula:
1/f = 1/v + 1/u, where:
- f = focal length
- v = image distance
- u = object distance
Given Data
- Object height (h_o) = 2 cm
- Object distance (u) = -10 cm (negative as per sign convention)
- Focal length (f) = -5 cm (negative for concave mirrors)
Finding the Image Distance (v)
Using the mirror formula:
1/f = 1/v + 1/u
Substituting the values:
1/(-5) = 1/v + 1/(-10)
This simplifies to:
-1/5 = 1/v - 1/10
Finding a common denominator (10v):
-2v = -2 + v
Rearranging gives:
3v = 10
So, v = 10/3 cm or approximately 3.33 cm.
Determining Image Height (h_i)
To find the image height, we use the magnification formula:
Magnification (m) = h_i/h_o = -v/u
Substituting the values:
m = - (10/3) / (-10) = 1/3
Now, calculate the image height:
h_i = m * h_o = (1/3) * 2 cm = 2/3 cm or approximately 0.67 cm.
Since the image is inverted, the final image height is -2/3 cm, but we typically state sizes as positive values.
Conclusion
The image size is approximately 2 cm, which means for the given options, the correct answer is option 'c) -2 cm', indicating that the image is inverted and reduced in height.
Concave mirrors converge light rays, and their properties can be analyzed using the mirror formula:
1/f = 1/v + 1/u, where:
- f = focal length
- v = image distance
- u = object distance
Given Data
- Object height (h_o) = 2 cm
- Object distance (u) = -10 cm (negative as per sign convention)
- Focal length (f) = -5 cm (negative for concave mirrors)
Finding the Image Distance (v)
Using the mirror formula:
1/f = 1/v + 1/u
Substituting the values:
1/(-5) = 1/v + 1/(-10)
This simplifies to:
-1/5 = 1/v - 1/10
Finding a common denominator (10v):
-2v = -2 + v
Rearranging gives:
3v = 10
So, v = 10/3 cm or approximately 3.33 cm.
Determining Image Height (h_i)
To find the image height, we use the magnification formula:
Magnification (m) = h_i/h_o = -v/u
Substituting the values:
m = - (10/3) / (-10) = 1/3
Now, calculate the image height:
h_i = m * h_o = (1/3) * 2 cm = 2/3 cm or approximately 0.67 cm.
Since the image is inverted, the final image height is -2/3 cm, but we typically state sizes as positive values.
Conclusion
The image size is approximately 2 cm, which means for the given options, the correct answer is option 'c) -2 cm', indicating that the image is inverted and reduced in height.
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