An object is positioned 24 cm from a spherical concave mirror of unknown focal l

Question

An object is positioned 24 cm from a spherical concave mirror of unknown focal length. The image that is formed is 30 cm from the mirror. Calculate the focal length. (Enter NONE if a particular answer docs not exist.) pusitive image distance negative image distance Is this answer unique? Yes, there is only one possible focal length. No, there are two possible focal lengths. Is the image real or virtual? The image is real. The image is virtual. Both images are real. Both images are virtual. One image is real and the other is virtual. The image is neither real nor virtual. If the object is 10 cm tall, determine the height of the image(s). postive image distance cm negative image distance cm

Explanation / Answer

here,

Sign Convension,
1.) Since, object is always placed in front of the mirror hence the sign of object is taken as negative.

2.) Since, the centre of curvature and focus lie in front of the concave mirror, so signs of radius of curvature and focal length are taken as negative in the case of concave mirror.

3.) When image is formed in front of the mirror, the distance of image is taken as – (negative) and when image is formed behind the mirror, the distance of image is taken as + (positive).

Therfore,
object distance, do = -24 cm
image distance, di = - 30 cm

Fromt thin Lens Equation, Solving for focal length, f
1/f = 1/do + -1/di
1/f = -1/24 -1/30
f = -13.33 cm ( -ve since it is a cocave mirror)

Part B:
There is only one positive value of focal length

Part C:
The image always Real in case of concave mirror

Part D:
if Height of object, ho = 10 cm

Since Magnification, m = -do/di = hi/ho
solving for image height, hi = -do*ho/di
hi = -(-24)*10/(-30)
hi = -8 cm

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