A convex mirror in a car has focal length 300cm if a cycle is located at 50cm from this mirror. Find the position nature magnification of cycle fromed in the mirror. Pless give the answer like you are giving board exam
Answers
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The image of cycle in the mirror is formed at a distance of 300/7 cm behind the mirror and is virtual, erect and is diminished by 6/7 times.
Given:
i) A convex mirror in a car has focal length 300cm.
ii) A cycle is located at 50cm from this mirror.
To find:
Position, nature and magnification of the image of cycle formed in the mirror.
Solution:
For a convex mirror, its focal length is positive.
Hence, f = +300cm
It is given that a cycle is located at 50cm from this mirror, and cycle here is the object.
Therefore, u = -50cm
Applying the mirror formula,
1/v + 1/u = 1/f
=> 1/(-50) + 1/v = 1/(+300)
=> -1/50 + 1/v = 1/300
=> 1/v = 1/50 + 1/300
=> 1/v = 6/300 + 1/300
=> 1/v = 7/300
=> v = +300/7 cm
Using the formula for magnification, m = -(v/u) we get
m = -(+300/7/(-50))
=> m = +300/(7*50)
=> m = +6/7
Since,
v > 0 => Image is formed behind the mirror and hence is virtual in nature.
m > 0 => Image is erect.
m < 1 => Image is diminished.
Therefore,
The image of cycle in the mirror is formed at a distance of 300/7 cm behind the mirror and is virtual, erect and is diminished by 6/7 times.
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