The image formed by a convex mirror of focal length 30 cm.Is a quarter the size of the obj.Then the distance of the object from the mirror .

Question

Answer

Given:

focal length of convex mirror = 30 cm

image size = quarter of the object size

To Find:

Distance of the object from the mirror

Solution:

Let the distance of the object from the mirror be 'u' and the size of the object be 'h'.

Using the mirror formula, we have:

1/f = 1/u + 1/v

where f is the focal length and v is the distance of the image from the mirror.

For a convex mirror, the image is always virtual, erect and diminished.

Therefore, we have:

v = -f (since the image is virtual and behind the mirror)

m = -v/u (where m is the magnification)

Given that the image size is quarter of the object size, we have:

m = -1/4

Substituting the values, we get:

-1/4 = -(-30)/u

u = 120 cm

Answer:

The distance of the object from the convex mirror is 120 cm.

Answer

The mirror formula is given as1/f = (1/v) + (1/u)  (1)heref = focal length = 30cmv = image distance u = object distancewe are given thathi = ho/4orhi / ho = 1/4hi = image heightho = object heightnow ashi / ho = -v/u = 1/4we getv = -u/4  so, using this in eq. (1), we get1/30 = -4/u + 1/uor1/30 = -3/uthus, the object distance will beu = -90 cm

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