Konvergentne leće – problemi i rješenja

1. A 5-cm high object is placed 5 cm from a 15-cm focal length konvergentan lens. Determine the image udaljenost, the magnification of the image, the image height and o properties of slika.

Poznato:

Žarišna duljina (f) = 15 cm

The plus sign indicates that the focal point is real or the rays pass through the point.

Visina objekta (h_o) = 5 cm

Udaljenost objekta (d_o) = 5 cm

tražen : udaljenost slike, the magnification of image, the image height and the properties of image

rješenje:

Formation of image by konvergentna leća :

Udaljenost slike (d_i)

1/d_i = 1/f – 1/d_o = 1/15 – 1/5 = 1/15 – 3/15 = -2/15

d_i = -15/2 = -7.5 cm

Znak minus označava da je slika virtualna ili da zrake ne prolaze kroz sliku.

Uvećanje slike (m)

m = - d_i / d_o = -(-7.5)/5 = 7.5/5 = 1.5

Znak plus označava da je slika uspravna.

Visina slike (h_i)

m =h_i / h_o

h_i = m h_o = (1.5)5 = 10/3 = 7.5 cm

Znak plus označava da je slika uspravna.

The properties of the image

- virtualan

- uspravan

- The image greater than the object

- The image distance is greater than the object distance

2. 10-cm high object is placed 30 cm from a 15-cm focal length konvergentan lens. Determine the image distance, the magnification of the image, the image height and o properties of slika.

Poznato:

Žarišna duljina (f) = 15 cm

The plus sign indicates that the focal point is real or the rays pass through the point.

Visina objekta (v) = 10 cm

Udaljenost objekta (s) = 30 cm

Htjela: The image distance, the magnification of the image, the image height and the properties of the image

rješenje:

Formation of the image by the converging lens :

Udaljenost slike (d_i)

1/d_i = 1/f – 1/d_o = 1/15 – 1/30 = 2/30 – 1/30 = 1/30

d_i = 30/1 = 30 cm

The plus sign indicates that the image is real or the zrake pass through the image.

Uvećanje slike (m)

m = - d_i / d_o = -(30)/30 = -30/30 = -1

Znak minus označava da je slika invertirana.

Visina slike (h_i)

m =h_i / h_o

h_i = m h_o = (-1)10 = -10 cm

Znak minus označava da je slika invertirana.

The properties of the image

- real or the rays pass through the image

- obrnut

- The image height is the same as the object height.

- The image distance is the same as the object distance.

3. 10-cm high object is placed 30 cm from a 20-cm focal length konvergentan lens. Determine the image distance, the magnification of the image, the image height and o properties of slika.

Poznato:

Žarišna duljina f) = 20 cm

The plus sign indicates that the focal point is real or the rays pass through the point.

Visina objekta (v) = 10 cm

Udaljenost objekta (d_o) = 30 cm

Traži se: Udaljenost slike, the magnification of image, the image height and the properties of image

rješenje:

Udaljenost slike (d_i)

1/d_i = 1/f – 1/d_o = 1/20 – 1/30 = 3/60 – 2/60 = 1/60

d_i = 60/1 = 60 cm

The plus sign indicates that the image is real or the rays pass through the image.

Uvećanje slike (m)

m = - d_i / d_o = -(60)/30 = -2

Znak minus označava da je slika invertirana.

The image is 2 times greater than the object.

Visina slike (h_i)

m =h_i / h_o

hi = m h_o = (-2)10 = -20 cm

Znak minus označava da je slika invertirana.

The properties of the image

- stvarne

- obrnut

- the image height is greater than the object height

- the image distance is greater than the object distance

4. Based on the figure below, determine the focal length of the converging lens!

Poznato:

Udaljenost objekta (d_o) = 20 cm

Udaljenost slike (d_i) = 30 cm

tražen : Žarišna duljina (F)

rješenje:

1/d_o + 1 /d_i = 1/f

d_o = object distance (plus znak jer rays pass through objekt)

d_i = image distance (plus znak jer rays pass through slika)

f = žarišna duljina (plus znak because rays pass through the focal point or the focal point is real)

The focal length :

1/f = 1/20 + 1/30 = 3/60 + 2/60 = 5/60

f = 60/5 = 12 cm

5. Object’s distance is 30 cm and the focal length is 20 cm. Determine the magnification of the image.

Poznato:

The focal length of the converging lens (f) = 20 cm

The plus sign indicates that the focal point is real or rays proći kroz slika.

Udaljenost objekta (d_o) = 30 cm

Traži se: Uvećanje slike (M)

rješenje:

Image distance :

1/d_i = 1/f – 1/do = 1/20 – 1/30 = 3/60 – 2/60 = 1/60

d_i = 60/1 = 60 cm

Uvećanje slike:

M = d_i / d_o = 60 cm / 30 cm = 60/30 = 2 puta

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