contestada

A 5.0 cm object is 6.0 cm from a convex lens, which has a focal length of 7.0 cm.
What is the distance of the image from the lens?

cm
What is the height of the image?

cm

Respuesta :

Answer : The distance of the image from the lens is, -42 cm

The height of the image is, 35 cm

Solution :

First we have to calculate the image distance.

Formula used :

[tex]\frac{1}{f}=\frac{1}{p}+\frac{1}{q}[/tex]

where,

f = focal length = 7 cm

p = object distance = 6 cm

q = image distance = ?

Now put all the given values in the above formula, we get the distance of the image from the lens.

[tex]\frac{1}{7cm}=\frac{1}{6cm}+\frac{1}{q}[/tex]

[tex]q=-42cm[/tex]

Therefore, the distance of the image from the lens is, 42 cm and the negative sign indicates that the image is virtual.

Now we have to calculate the height of the image.

Formula used :

[tex]\frac{h}{h'}=\frac{p}{q}[/tex]

where,

h = height of object = 5 cm

h' = height of image = ?

Now put all the given values in this formula, we get the height of the image.

[tex]\frac{5cm}{h'}=\frac{6cm}{-42cm}=-35cm[/tex]

Therefore, the height of the image is, 35 cm and the negative sign indicates that the image is inverted.

Eduard22sly

A. The distance of the image from the lens is –42 cm.

B. The height of the image is 35 cm

Data obtained from the question

  • Height of object (Hₒ) = 5 cm
  • Object distance (u) = 6 cm
  • Focal length (f) = 7 cm
  • Image distance (v) =?
  • Height of image (Hᵢ) =?

A. How to determine the image distance

The image distance is defined as the distance of the image from the lens. Thus, it can be obtained as follow:

  • Object distance (u) = 6 cm
  • Focal length (f) = 7 cm
  • Image distance (v) =?

1/v = 1/u – 1/f (convex lens

v = (uf) / (u –f)

v = (6 × 7) / (6 – 7)

v = 42 / – 1

v = –42 cm

B. How to determine the height of the image.

The height of the image is the height of the image as displayed by the lens. It can be obtained as follow:

  • Height of object (Hₒ) = 5 cm
  • Object distance (u) = 6 cm
  • Focal length (f) = 7 cm
  • Image distance (v) = –42 cm
  • Height of image (Hᵢ) =?

v / u = Hᵢ / Hₒ

–42 / 6 = Hᵢ / 5

–7 = Hᵢ / 5

Cross multiply

Hᵢ = –7 × 5

Hᵢ = –35 cm

NOTE: The negative sign indicates that the image is a virtual image.

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