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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 to the size of the truck and also find the position and nature of the image formed.

2 Answers

5 votes

Answer:

Step-by-step explanation:The car will appear to be 0.8 m behind the mirror.

User Igor Kondrasovas
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2 votes

Answer:

The size of the image is 4/9 times larger than the actual size of the truck.

the image is magnified and virtual

Explanation:

We can use the mirror formula to find the position and nature of the image formed by the rear-view mirror in the car:

1/f = 1/u + 1/v

where:

f = radius of curvature of the mirror = 4m (given)

u = distance of the object (the truck) from the mirror = -5m (negative sign indicates that the object is behind the mirror)

v = distance of the image from the mirror (positive sign indicates that the image is in front of the mirror)

Substituting the given values, we get:

1/4 = 1/-5 + 1/v

Simplifying this equation, we get:

v = m

v=20/9 m

This means that the image of the truck is formed at a distance of 20/9meters from the rear-view mirror, behind the driver's seat.

To find the size of the image relative to the size of the truck, we can use the magnification formula:

m = v/u

Substituting the values we get:

m =(-20/9) / (-5) = 4/9

This means that the image of the truck formed by the rear-view mirror in the car is 4/9 times larger than the actual size of the truck.

So, the image is magnified and virtual (since the image is formed behind the mirror), and its distance from the mirror is 20/9 meters. The size of the image is 4/9 times larger than the actual size of the truck.

User Bruno Carballo
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7.6k points