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An object is placed at the centre of curvature of a concave mirror. The distance between its image
and the pole is
- a)equal to f
- b)between f and 2f
- c)equal to 2f
- d)greater than 2f
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
An object is placed at the centre of curvature of a concave mirror. Th...
Explanation:
The given situation can be represented as follows:
Here, C is the centre of curvature of the concave mirror, F is the focus, and P is the pole.
Now, let us consider the path of light rays from the object to the mirror and then to its image.
- The light rays from the object are parallel to the principal axis and fall on the mirror.
- At the point of incidence, the light rays are reflected and converge towards the focus F.
- However, since the object is placed at the centre of curvature C, the reflected rays pass through F and become parallel to the principal axis.
- These parallel rays then converge at the position of the image I.
Therefore, we can see that the image is formed at a distance equal to twice the focal length from the mirror.
- From the mirror formula:
1/f = 1/v + 1/u
where f is the focal length, v is the image distance, and u is the object distance.
- In this case, since the object is placed at C, u = -2f (negative sign indicates that it is on the opposite side of the mirror).
- We want to find v, the distance between the image and the pole.
- Substituting the given values, we get:
1/f = 1/v - 1/2f
Multiplying both sides by vf2, we get:
2f = v + f
Therefore, v = 2f - f = f.
Hence, the distance between the image and the pole is equal to the focal length of the mirror, which is option C.
The given situation can be represented as follows:
Here, C is the centre of curvature of the concave mirror, F is the focus, and P is the pole.
Now, let us consider the path of light rays from the object to the mirror and then to its image.
- The light rays from the object are parallel to the principal axis and fall on the mirror.
- At the point of incidence, the light rays are reflected and converge towards the focus F.
- However, since the object is placed at the centre of curvature C, the reflected rays pass through F and become parallel to the principal axis.
- These parallel rays then converge at the position of the image I.
Therefore, we can see that the image is formed at a distance equal to twice the focal length from the mirror.
- From the mirror formula:
1/f = 1/v + 1/u
where f is the focal length, v is the image distance, and u is the object distance.
- In this case, since the object is placed at C, u = -2f (negative sign indicates that it is on the opposite side of the mirror).
- We want to find v, the distance between the image and the pole.
- Substituting the given values, we get:
1/f = 1/v - 1/2f
Multiplying both sides by vf2, we get:
2f = v + f
Therefore, v = 2f - f = f.
Hence, the distance between the image and the pole is equal to the focal length of the mirror, which is option C.
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Community Answer
An object is placed at the centre of curvature of a concave mirror. Th...
When the object is placed at the center of curvature, the image is formed at the center of curvature and we know that the relation between radius of curvature and focal length is R= 2F ( R is used to show radius of curvature And F is the focal length ) if you will notice the its ray diagram then u could see that radius of curvature is always twice of Focal length.
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