the radius of curvature of a convex mirror used on a automobile is 200cm.A bus is coming behind it at a distance of 3.5m calculate (1)position (2)the size of the image relative to the bus.Also comment on the nature of image
the radius of curvature of a convex mirror used on a automobile is 200cm.A bus is coming behind it at a distance of 3.5m calculate (1)position (2)the size of the image relative to the bus.Also comment on the nature of image
Given :
R =200 cm = 2 m
=> focal length, f = R/2
=> f = +1 m (convex mirror)
Object distance, u = -3.5 m (by sign convection -- bus is behind)
To find :
Position of the image, magnification and nature of the image.
Solution :
1/v + 1/u = 1/f
1/v = 1/f - 1/u
1/v = 1/1 - 1/(-3.5)
1/v = (3.5 + 1) / 3.5
1/v = 4.5 / 3.5
v = 3.5 / 4.5
v = 0.77 m
Therefore, the image will be formed at a distance of 0.77 m infront of the mirror.
Magnification, m = h'/h
= -v/u
m = - (0.77) / (-3.5)
m = 0.77 / 3.5
m = 0.22 m
=> m < 1
Therefore, the image will be diminished, virtual and erect.
Given :
R =200 cm = 2 m
=> focal length, f = R/2
=> f = +1 m (convex mirror)
Object distance, u = -3.5 m (by sign convection -- bus is behind)
To find :
Position of the image, magnification and nature of the image.
Solution :
1/v + 1/u = 1/f
1/v = 1/f - 1/u
1/v = 1/1 - 1/(-3.5)
1/v = (3.5 + 1) / 3.5
1/v = 4.5 / 3.5
v = 3.5 / 4.5
v = 0.77 m
Therefore, the image will be formed at a distance of 0.77 m infront of the mirror.
Magnification, m = h'/h
= -v/u
m = - (0.77) / (-3.5)
m = 0.77 / 3.5
m = 0.22 m
=> m < 1
Therefore, the image will be diminished, virtual and erect.
