An object 4 cm in size is placed at a distance of 25 cm from a concave mirror of focal length 15 cm. At what distance from the mirror should the screen be kept so that a sharp image of the object can be obtained on screen? Find the nature and height of the image.

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37.5 cm, real, inverted and magnified, 6cm

47.5 cm, real, inverted and magnified, 6cm

38.5 cm, real, inverted and magnified, 6cm

None of these

answer is A.

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Detailed Solution

Concept: To solve this question, we can use the replicate formulation, which incorporates 3 values: the focal period of the replicate (f) , the gap of the item from the replicate (u) , and the gap of the photograph from the replicate (d) (v). If any of them are known, the formulation may be used to calculate the third.

Given that, the size of the object is

the distance between the object and the mirror is u = 25cm, and the focal length of the mirror is

We need to figure out how far away the screen should be placed in order to get a clear image of the object.
We know that the object distance, u, is always negative, and the mirror in this case is concave
As a result, the focal length is also regarded as negative.
From the mirror formula,

magnification,

To get a sharp image,

The image is real, inverted and magnified.
The height of the image is -6cm.
Hence, option 1 is correct.

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