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A point object ' O ' is at the centre of curvature of a concave mirror. The mirror starts to move at a speed u, in a direction perpendicular to the principal axis. Then the initial velocity of the image is:
  • a)
    2 u, in the direction opposite to that of mirror's velocity
  • b)
    2 u, in the direction same as that of mirror's velocity
  • c)
    zero
  • d)
    u, in the direction same as that of mirror's velocity.
Correct answer is option 'B'. Can you explain this answer?
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A point object O is at the centre of curvature of a concave mirror. ...
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A point object O is at the centre of curvature of a concave mirror. ...
Initial conditions

- The point object O is at the centre of curvature of a concave mirror.
- The mirror starts to move at a speed u, in a direction perpendicular to the principal axis.

Explanation

When the mirror starts to move, the point object O will also start to move in the same direction as the mirror's velocity. As a result, the image formed by the mirror will also start to move.

Since the point object O is at the centre of curvature of the concave mirror, the image formed by the mirror will also be located at the centre of curvature. This is because the light rays from the point object O will be reflected back along the same path due to the mirror's spherical shape.

The relationship between the velocity of the image (vi), the velocity of the mirror (vm), and the velocity of the point object O (vo) can be given by the mirror formula:

1/f = 1/vi + 1/vo

Since the point object O is at the centre of curvature, the object distance (vo) is equal to twice the focal length (f):

vo = 2f

Substituting this into the mirror formula, we get:

1/f = 1/vi + 1/(2f)

Simplifying the equation, we find:

1/vi = 1/f - 1/(2f)

1/vi = 2/(2f) - 1/(2f)

1/vi = 1/(2f)

Therefore, the initial velocity of the image (vi) is equal to half the velocity of the mirror (vm):

vi = vm/2

Since the mirror is moving at a speed u, in a direction perpendicular to the principal axis, the velocity of the mirror (vm) is equal to u. Therefore, the initial velocity of the image (vi) is:

vi = u/2

So, the correct answer is option B: 2u, in the direction same as that of the mirror's velocity.
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A point object O is at the centre of curvature of a concave mirror. The mirror starts to move at a speed u, in a direction perpendicular to the principal axis. Then the initial velocity of the image is:a)2 u, in the direction opposite to that of mirrors velocityb)2 u, in the direction same as that of mirrors velocityc)zerod)u, in the direction same as that of mirrors velocity.Correct answer is option 'B'. Can you explain this answer?
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