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The driving mirror of a car has a radius of curvature of 1m. A vehicle behind th...


Question

The driving mirror of a car has a radius of curvature of 1m. A vehicle behind the car is 4m from the mirror. Find the image distance behind the mirror.

Options

A) 8/7

B) 4/9

C) 9/2

D) 4/7


The correct answer is B.

Explanation:

A driving mirror is always a convex mirror which is always of negative focal length and always forms a virtual image

Thus if r = 1m = 100cm
f = 1/2 = -50
∴ if U = 4cm = 400cm
f = -50cm

∴1/u + 1/v = 1/f
1/400 + 1/v = -1/50
∴ -1/v = 1/400 + 1/50
-1/v = (1 + 8)/400 = 9/400
∴ v = -400/9
v = 4/9


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Dicussion (1)

  • A driving mirror is always a convex mirror which is always of negative focal length and always forms a virtual image

    Thus if r = 1m = 100cm
    f = 1/2 = -50
    ∴ if U = 4cm = 400cm
    f = -50cm

    ∴1/u + 1/v = 1/f
    1/400 + 1/v = -1/50
    ∴ -1/v = 1/400 + 1/50
    -1/v = (1 + 8)/400 = 9/400
    ∴ v = -400/9
    v = 4/9

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