a motor car fitted with a convex driving mirror of focal length 20 cm.a second motor car 2.1m board and 1.05m high is 4m behind the first car .what is the size of the image of the second car as seen in the mirror of the first ??

To find the size of the image of the second car as seen in the convex mirror of the first car, we can use the mirror formula and the magnification formula. Let's break this down step by step.

Understanding the Mirror Formula

The mirror formula for a convex mirror is given by:

1/f = 1/v + 1/u

Where:

• f is the focal length of the mirror (positive for convex mirrors).
• v is the image distance (positive for virtual images in convex mirrors).
• u is the object distance (negative as per the sign convention).

Given Data

From the problem, we know:

• Focal length, f = +20 cm
• Distance between the two cars, d = 4 m = 400 cm
• Height of the second car, h = 1.05 m = 105 cm

Calculating Object Distance

The object distance u for the second car, as seen from the first car's mirror, is:

u = -d = -400 cm

Finding Image Distance

Now, we can substitute the values into the mirror formula:

1/f = 1/v + 1/u

Substituting the known values:

1/20 = 1/v + 1/(-400)

This simplifies to:

1/20 = 1/v - 1/400

To solve for 1/v, we can rearrange the equation:

1/v = 1/20 + 1/400

Finding a common denominator (which is 400):

1/v = 20/400 + 1/400 = 21/400

Thus, we find:

v = 400/21 ≈ 19.05 cm

Calculating Magnification

The magnification m of the image is given by:

m = -v/u

Substituting the values we have:

m = - (400/21) / (-400) = 1/21

Finding the Size of the Image

Now, we can find the height of the image h' using the magnification formula:

h' = m × h

Substituting the values:

h' = (1/21) × 105 cm ≈ 5 cm

Final Result

The size of the image of the second car as seen in the mirror of the first car is approximately 5 cm. This image will be virtual, upright, and smaller than the actual height of the second car due to the nature of the convex mirror.