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the distance between the object and it's inverted image by a concave mirror is 15 cm if the magnification produced by the mirror is _2.use the mirror formula to determine the object distance image distance and focal length of the mirror
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the distance between the object and it's inverted image by a concave m...
Given Information
- Distance between the object and its inverted image = 15 cm
- Magnification (m) = -2 (negative sign indicates an inverted image)
Mirror Formula
The mirror formula relates object distance (u), image distance (v), and focal length (f):
1/f = 1/v + 1/u
Magnification Formula
The magnification (m) is given by:
m = -v/u
Calculating Image Distance (v)
Using the magnification formula:
-2 = -v/u
=> v = 2u
Now, we know the distance between the object and the image:
v - u = 15 cm
Substituting v:
2u - u = 15
=> u = 15 cm
=> v = 2u = 30 cm
Calculating Focal Length (f)
Now, substituting the values of u and v into the mirror formula:
1/f = 1/v + 1/u
=> 1/f = 1/30 + 1/(-15)
=> 1/f = 1/30 - 2/30
=> 1/f = -1/30
=> f = -30 cm
Summary of Results
- Object distance (u) = -15 cm (Conventionally negative for concave mirrors)
- Image distance (v) = -30 cm (Negative indicates real and inverted image)
- Focal length (f) = -30 cm (Indicating a concave mirror)
This detailed analysis provides the necessary calculations for the concave mirror's properties based on the given conditions.
- Distance between the object and its inverted image = 15 cm
- Magnification (m) = -2 (negative sign indicates an inverted image)
Mirror Formula
The mirror formula relates object distance (u), image distance (v), and focal length (f):
1/f = 1/v + 1/u
Magnification Formula
The magnification (m) is given by:
m = -v/u
Calculating Image Distance (v)
Using the magnification formula:
-2 = -v/u
=> v = 2u
Now, we know the distance between the object and the image:
v - u = 15 cm
Substituting v:
2u - u = 15
=> u = 15 cm
=> v = 2u = 30 cm
Calculating Focal Length (f)
Now, substituting the values of u and v into the mirror formula:
1/f = 1/v + 1/u
=> 1/f = 1/30 + 1/(-15)
=> 1/f = 1/30 - 2/30
=> 1/f = -1/30
=> f = -30 cm
Summary of Results
- Object distance (u) = -15 cm (Conventionally negative for concave mirrors)
- Image distance (v) = -30 cm (Negative indicates real and inverted image)
- Focal length (f) = -30 cm (Indicating a concave mirror)
This detailed analysis provides the necessary calculations for the concave mirror's properties based on the given conditions.
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the distance between the object and it's inverted image by a concave mirror is 15 cm if the magnification produced by the mirror is _2.use the mirror formula to determine the object distance image distance and focal length of the mirror Related: NCERT Solutions - Light, Reflection and Refraction?
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