Question

A convex mirror is used in a bus has radius of curvature 3.5m.If the driver of the bus locates a car at 10.0m behind the bus, find the position, nature and size of the image of the car.

Answer 1

Explanation:

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Answer 2

Given: radius of Curvature - R = 3.5m

Object distance - u = -10m

To Find:

image distance - v = ?

size and nature of the image

Solution:

Formula used:

• focal length - f = R/2
• 1/f = 1/v + 1/u
• magnification - m = - height of image/height of object = -v/u

Applying the above formulas to calculate the focal length "f" of the mirror and image distance"v".

f = R/2 = 3.5/2

f = 1.75

1/f = 1/v + 1/u

1/1.75 = 1/v - 1/10

1/v = 1/1.75 + 1/10

1/v = 0.57 + 0.1

1/v = 0.67

1/v = 67/100

v = 100/47

v = 1.5m

Applying the formula of magnification to find the nature of the image.

m = - v/u

m = - 1.5/-10

m = 0.15

Hence, the image is erect, virtual as the magnification is positive, and diminished as m < 1.

And image position is 1.5m.