An object 5cm is placed 30cm in front of a concave mirror.The image is 60cm in front of the mirror.Find (a) the focal length of the mirror.(b) the magnification.(c)the size of the image
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To find the answers to these questions, we will use the mirror formula and magnification formula.
(a) The mirror formula is given by:
1/f = 1/v - 1/u
where f is the focal length of the mirror, v is the image distance (in this case, 60 cm), and u is the object distance (in this case, 30 cm).
Substituting the given values into the formula:
1/f = 1/60 - 1/30
Simplifying the equation:
1/f = (2 - 1)/60 = 1/60
Therefore, the focal length of the mirror is f = 60 cm.
(b) The magnification formula is given by:
magnification (m) = -v/u
Substituting the given values into the formula:
m = -(60/30) = -2
Therefore, the magnification is -2. The negative sign indicates that the image is inverted.
(c) The size of the image can be found using the magnification formula and the size of the object.
m = h'/h
where h' is the height of the image and h is the height of the object.
Given that the object's size is 5 cm, we can rearrange the formula to solve for h':
h' = m * h
= -2 * 5
= -10 cm
The negative sign indicates that the image is also inverted. Therefore, the size of the image is -10 cm.
There is a formula you should have seen by now, for both mirros and lebneses.
1/Do + 1/Di = 1/f
Do is the object distance and Di is the image distance from the mirror., in this case.
1/30 + 1/60 = 1/f
Solve for the focal length f.
For the size of the image, use the fact that the magnification is
Di/Do = 2
That makes the image size 10 cm