The radius of curvature of a rear- view mirror in a car is 4m. If a truck is behind the car,located 5m from the rear-view mirror of the car. Calculate the size of the image relative tothe size of the truck and also find the position and nature of the image formed.

To calculate the size of the image relative to the size of the truck, we can use the mirror equation:

1/f = 1/v + 1/u

Where: f = focal length (radius of curvature) v = image distance from the mirror u = object distance from the mirror

Given that the radius of curvature (f) is 4m and the object distance (u) is 5m, we can substitute these values into the equation:

1/4 = 1/v + 1/5

To solve for v, we can rearrange the equation:

1/v = 1/4 - 1/5 1/v = (5 - 4) / (4 * 5) 1/v = 1/20 v = 20m

Now that we have the image distance (v), we can calculate the size of the image relative to the size of the truck. The magnification (M) is given by the equation:

M = -v/u

Substituting the values:

M = -20/5 M = -4

The negative sign indicates that the image is inverted relative to the object.

Therefore, the size of the image is 4 times larger than the size of the truck.

As for the position and nature of the image formed, since the image distance (v) is positive, the image is formed on the same side as the object (behind the mirror). The negative magnification (M) indicates that the image is inverted.