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An object is placed in front of a convex mirror, and the size of the image is one-third that of the object. What is the ratio (d,/f) of the object distance to the focal length of the mirror?

Respuesta :

Answer:

The ratio of the object distance to the focal length of the mirror is 4:1.

Explanation:

Given that,

The size of the image is one-third that of the object.

We need to calculate the focal length of the mirror

Using formula of mirror

[tex]\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}[/tex]

Where, v = image distance

u = object distance

Put the value into the formula

[tex]\dfrac{1}{f}=\dfrac{3}{u}+\dfrac{1}{u}[/tex]

[tex]\dfrac{1}{f}=\dfrac{4}{u}[/tex]

[tex]f = \dfrac{u}{4}[/tex]

We need to calculate the ratio of the object distance to the focal length of the mirror

[tex]\dfrac{u}{f}=\dfrac{4u}{u}[/tex]

[tex]\dfrac{u}{f}=\dfrac{4}{1}[/tex]

Hence, The ratio of the object distance to the focal length of the mirror is 4:1.

Eduard22sly

The ratio of the object distance to the focal length of the mirror is 4:1

Data obtained from the question

  • Magnification (m) = ⅓
  • Ratio of object distance to the focal length =?

How to determine the object distance

  • Magnification (m) = –⅓ (for convex mirror)
  • Image distance (v) =?

m = v/u

–⅓ = v/u

Cross multiply

v = –u/3

How to determine the ratio

  • Image distance (v) = –u/3
  • Ratio of object distance to the focal length =?

1/f = 1/u – 1/v

1/f = 1/u – [1÷ –u/3]

1/f = 1/u – (–3/u)

1/f = 1/u + 3/u

1/f = (1 + 3) / u

1/f = 4/u

Cross multiply

u / f = 4

u : f = 4 : 1

Thus, the ratio of object distance to the focal length is 4:1

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