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A 17.0 cm tall cup is placed 75.5 cm away from the center of a concave mirror with a focal length of 39.0 cm. What is the height of the cup's mirror image?

Respuesta :

Explanation:

It is given that,

Height of the object, h = 17 cm

Object distance, u = -75.5 cm

Focal length of the concave mirror, f = -39 cm

We need to find the height if the cup's mirror image. Let v is the image distance. Using mirror's equation as :

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

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

[tex]\dfrac{1}{(-39)}-\dfrac{1}{(-75.5)}=\dfrac{1}{v}[/tex]

v = −80.67 cm

Let h' is the magnification of the mirror. The magnification of mirror is given by:

[tex]m=\dfrac{-v}{u}=\dfrac{h'}{h}[/tex]

[tex]h'=\dfrac{-vh}{u}[/tex]

[tex]h'=\dfrac{-(-80.67)(17)}{-75.5}[/tex]

h' = −18.16 cm

So, the image of cup is 18.16 cm tall and it is inverted. Hence, this is the required solution.

Eduard22sly

The height of the cup's mirror image obtained is 0.92 cm

Data obtained from the question

  • Height of object (Hₒ) = 17 cm
  • Object distance (u) = 75.5 cm
  • Focal length (f) = 39 cm
  • Height of image (Hᵢ) =?

How to determine the image distance

  • Object distance (u) = 75.5 cm
  • Focal length (f) = 39 cm
  • Image distance (v) =?

1/v = 1/f – 1/u

1/v = 1/39 – 1/75.5

v =  (39 × 75.5) / (75.5 – 39)

v = 4.1 cm

How to determine the image hei

  • Height of object (Hₒ) = 17 cm
  • Object distance (u) = 75.5 cm
  • Focal length (f) = 39 cm
  • Image distance (v) = 4.1 cm
  • Height of image (Hᵢ) =?

Hᵢ / Hₒ = v / u

Hᵢ / 17  = 4.1 / 75.5

Cross multiply

Hᵢ = 17 × (4.1 / 75.5)

Hᵢ = 0.92 cm

Learn more about mirror equation:

https://brainly.com/question/12569476

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