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Rays of the Sun converge at a point of 30┬аcm in front of a concave mirror. Where should the object be placed so that the size of the image is equal to the size of the object?
60┬аcm in front of the mirror
Between 30 and 60┬аcm in front of the mirror
More than 30┬аcm in front of the mirror
30┬аcm in front of the mirror
60┬аcm in front of the mirror
When rays of the Sun (effectively at infinity) converge at a point in front of a concave mirror, that point is the focus of the mirror. Thus, the focal length f is 30┬аcm, and the radius of curvature R=2f=60┬аcm. To obtain an image of the same size as the object, the object must be placed at the center of curvature (C).
When rays of the Sun (effectively at infinity) converge at a point in front of a concave mirror, that point is the focus of the mirror. Thus, the focal length f is 30┬аcm, and the radius of curvature R=2f=60┬аcm. To obtain an image of the same size as the object, the object must be placed at the center of curvature (C).
Think of the mirror like a spotlight: if you want the reflection to be exactly the same size as the light source, you have to place the light at the mirror's 'balance point' (the center of curvature) so the rays reflect back along the same path.
f=2RтАЛ тАФ Relationship between focal length and radius
m=hoтАЛhiтАЛтАЛ=тИТuvтАЛ тАФ Magnification formula where тИгmтИг=1 at u=2f
In a concave mirror, the image is equal in size to the object only when the object is placed exactly at the center of curvature (2f). Since the Sun's rays converge at 30┬аcm, the focal length f=30┬аcm. Therefore, the center of curvature is at R=2f=2├Ч30=60┬аcm from the pole of the mirror.
Sun rays coming from infinity converge at the focus (f = 30 cm).
For an object, size of image equals size of object only at 2f.
Therefore, u=2├Ч30=60┬аcm.
Used in laboratory experiments for determining focal length.
Used in optical instruments requiring same-sized reproduction.
The focal length of a concave mirror is taken as negative in Cartesian sign convention, but the distance f is given as magnitude.
Option D is wrong because at 30 cm (the focus), the image is formed at infinity.
A is correct тАФ The object should be placed at the center of curvature, which is twice the focal length (2f=60┬аcm).
Whenever you see 'Sun rays converge', immediately identify the distance as the focal length f. Always remember R=2f for spherical mirrors!
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