A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. give the location of the image and the magnification. describe what happens as the needle is moved farther from the mirror.

Question: A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. give the location of the image and the magnification. describe what happens as the needle is moved farther from the mirror. 

To find the location of the image and the magnification in this scenario, we can use 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.

Given:

Focal length (f) = +15 cm (since it's a convex mirror)

Object distance (u) = -12 cm (negative because the object is placed in front of the mirror)

Needle height (h) = 4.5 cm

Plugging in the values into the formula, we can solve for v:

1/15 = 1/v - 1/-12

1/15 = (12 - v)/(-12v)

-12v = 15(12 - v)

-12v = 180 - 15v

3v = 180

v = 60 cm

The location of the image is 60 cm behind the mirror.

To find the magnification (m), we can use the formula:

m = -v/u

Plugging in the values:

m = -60/-12

m = 5

The magnification is 5, indicating that the image is magnified five times compared to the size of the object.

As the needle is moved farther from the mirror, the object distance (u) increases. This will affect the image distance (v) and magnification (m). If the object distance becomes larger, the image distance will also increase, leading to a smaller and less magnified image. The magnification will decrease accordingly.

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