A convex mirror used for rear view on an automobile has a radius of curvature of 6 m. If a car is located at 10 m from this mirror, find the position, nature and size of the image.?

Question

Answer

Given:
- Radius of curvature of convex mirror, R = 6m
- Object distance, u = -10m (negative sign indicates object is placed in front of the mirror)

To find:
- Position, nature and size of the image formed by the mirror.

Solution:
Step 1: Using mirror formula, we can find the image distance (v).

1/f = 1/u + 1/v where f = R/2 (for a spherical mirror)

1/(R/2) = 1/u + 1/v

v = (R/2) * (1 - u/R)

v = (6/2) * (1 + 10/6) = 7m

The image is formed at a distance of 7m from the mirror.

Step 2: Using magnification formula, we can find the magnification (m) of the image formed.

m = -v/u

m = -7/-10 = 0.7

The negative sign indicates that the image is formed behind the mirror and it is virtual (not real). The magnification tells us that the image is smaller than the object.

Step 3: Using the mirror formula again, we can find the size of the image formed.

1/v - 1/u = 1/f

1/v = 1/f + 1/u

1/v = 1/3 + 1/-10

v = -15/7m

The size of the image can be found using the magnification formula.

m = hi/ho = -v/u

hi = m * ho

hi = 0.7 * 1m (Assuming the height of the object is 1m)

hi = 0.7m

The image formed is virtual, erect and smaller than the object. It is formed at a distance of 7m behind the mirror and its height is 0.7m.

Answer

The image will be between focus and pole and it will be erect and diminished

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