the radius of curvature of a convex mirror used as a rear view mirror in a moving car is '20' m a truck is coming from behind it at a distance of 3.5 metre calculate the a)position b)size of the image relative to the size of truck what will be the nature of the image.
Answers
Given :
- Radius of curvature, r = 20 m
- Distance of truck from mirror, u = 3.5 m
To find :
- Position of image, v
- Size of image relative to size of truck, magnification
- Nature of image
Solution:
Radius of curvature is 20 meter, its focal length will be:
→ focal length = Radius of curvature/2
→ Focal length = 20m/2
→ Focal length = 10 m
Now applying mirror formula ::
→ 1/f = 1/v - 1/u
→ 1/10m = 1/v - 1/3.5m
→ 1/10m + 1/3.5m = 1/v
→ (7 + 20)/70m = 1/v
→ 27/70 m = 1/v
→ v = 70m/27
→ v = 2.6 m approx.
So the position of image is 2.6 m from back of the mirror.
Now applying formula for magnification ::
→ m = -v/u
→ m = -(2.6m)/(3.5m)
→ m = -0.74
Since, the magnification is less than 1, the image formed will be smaller than the size of object i.e truck and the negative sign donates that the image formed will be inverted.
Nature of image is real and inverted.
Explanation:
Given : The radius of curvature of a convex mirror used as a rear view mirror in a moving car is 20m a truck is coming from behind it at the distance of 3.5m.
To find : position , size of the image Relative to the size of the truck . what will be the nature of the image ?
Solution:
R = 20
R = 20/5
R = 10
u = -3.5m
We know that
1/v + 1/u = 1/f
1/v = 1/(-3.5) = 1/10
1/v = 1/10 + 1/3.5m
1/v = ( 7 + 20 )/70m
1/v = 27/70m
v = 70m/27
v= 2.6m approx...
Position of the image is 2.6m from behind the mirror.
Now applying the formula for magnification:
m = -v/u
m= -(2.6m) / (3.5m)
m = -0.74
The magnification is less than 1. The image formed will be smaller than the size of the object i.e truck and the negative sign donates that the image formed will be in inverted.
Nature of the image is real and inverted.
Hope it helps you..........