A converging mirror of focal length 20cm forms an image which is two times
the size of the object. Calculate two possible distances of the object from
the mirror.
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To calculate the two possible distances of the object from the mirror, we can use the mirror equation:
1/f = 1/v - 1/u
where:
f = focal length of the mirror
v = image distance from the mirror
u = object distance from the mirror
Given:
f = 20 cm
v = -2u (the negative sign indicates that the image is formed on the same side as the object, which is a property of a converging mirror)
magnification (M) = v/u = -2
Substituting the values into the mirror equation, we get:
1/20 = 1/(-2u) - 1/u
To eliminate the fractions, we can find a common denominator and simplify the equation:
(u - 2u)/20u = -1/20
Simplifying further:
-u/20u = -1/20
Now, we can cross-multiply and solve for u:
-20 = -u
Solving for u, we find:
u = 20 cm
Therefore, one possible distance of the object from the mirror is 20 cm.
To find the second possible distance, we can use the magnification formula:
M = v/u = -2
Since the magnification is negative, it indicates that the image is inverted. This suggests that the object is placed between the mirror and its focal point (f). Therefore, the second possible distance (u') can be calculated as:
M = v/u'
-2 = -2(20 + u')
Simplifying the equation:
-2 = -40 - 2u'
Rearranging and solving for u', we find:
2u' = 40 - 2
2u' = 38
u' = 38/2
u' = 19
Therefore, the second possible distance of the object from the mirror is 19 cm.