Question

A bus uses a convex mirror as view finder whose radius of curvature is 4 m. A car is
coming behind the bus, which is at a distance of 20 m. What will be the position and size of the image of the car when observed by the driver of the bus through the convex mirror?​

Answer 1

Given:-

→ Radius of curvature of the mirror = 4m

→ Position of the car = 20m[behind bus]

To find:-

→ Position and size of the image of the

car that can be observed through the

convex mirror.

Solution:-

Firstly, let's calculate the focal length of the convex mirror :-

⇒f = R/2

⇒f = 4/2

⇒f = 2 m

Now according to mirror formula, we have :-

1/u + 1/v = 1/f

Where :-

• u is position of the object.

• v is position of the image.

• f is the focal length of the mirror.

Since, the mirror is convex :-

∴ f = + 2m

∴ u = -20m

⇒1/v = 1/f - 1/u

⇒1/v = 1/2 - 1/(-20)

⇒1/v = 0.5 - (-0.05)

⇒1/v = 0.55

⇒v = 1/0.55

⇒v = 1.82m

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Now, we know that :-

m = -(v/u)

⇒m = -[1.82/(-20)]

⇒m = -[-0.091)

⇒m = + 0.091

________________________________

Thus :-

• Position of the image of the car is

1.82m when observed by the driver of

the bus through the mirror.

• Size of the image is 0.091 times the

size of the object.