the radius of curvature of a convex mirror used on a moving automobile is 2.0m. A truck is coming behind it at a constant distance of 3.5m. Calculate the position and the size of image relative to the size of the truck .What will be the nature of the image?
Answers
u = -3.5 m
Using mirror formula,
1 ÷ -3.5 m + 1 ÷ v = 1 ÷ 1 m
1 ÷ v = 1 m + 1 ÷ 3.5 m
1 ÷ v = (3.5 + 1) m ÷ 3.5
1 ÷ v = 4.5 m ÷ 3.5
1 ÷ v = 9 ÷ 7 m
v = 7 ÷ 9 m
v = 0.78 m
Image will be virtual, erect and smaller than object.
The distance of the image is 0.7m and the magnification is 0.2.
Given,
A convex mirror whose radius of curvature is 2m. A truck is at a distance of 3.5m.
To find,
Position, size of image relative to the size of object and the nature of the image.
Solution,
As the truck is at a constant distance, we will assume them to be stationary because no change is there in the object's distance or height.
The object distance(u)=-3.5m
We know, R=2f
where R is the Radius of curvature and f is the focal length.
2=2f
f=1 m.
Let the image distance be v m.
According to the mirror formula,
1/v+1/u=1/f.
1/v=1/f-1/u
1/v=1-1/(-3.5)
=1+1/3.5
=4.5/3.5
=45/35
v=35/45.
=0.7m.
The size of the image relative to the size of the object is the Magnification and it can also be found out by image and object distance.
magnification= -v/u
=-0.7/-3.5
=0.2
The distance of the image is 0.7m and the magnification is 0.2.
Nature, The nature of the image will be virtual and erect.
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