Answer to Question #122566 in Optics for Anelisa

Question

A flower is placed 30 cm in front of a converging lens of focal length 20 cm.

Calculate the magnification of the image.

2. A diverging mirror with a focal length of 25 cm has a magnification of 0.50. How far apart are the object and the image?

Answer 1

1. According to the thin lens approximation, the magnification of the lens is given by (https://en.wikipedia.org/wiki/Lens#Thin_lens_approximation):

$$M = \dfrac{f}{f-S_1}$$

or

$$M = -\dfrac{S_2}{S_1}$$

where $f = 20 cm$ is the focal length, $S_1 = 30 cm$ is the distance from the  flower to the lens and $S_2$ .is the distance from the image to the lens. Substituting the values into the first equation, obtain:

$$M = \dfrac{20}{30-20} = 2$$

2. According to the first formula:

$$0.5 = \dfrac{25}{25-S_1}\\ S_1 = -25 cm$$

Now let's use the second formula:

$$0.5= -\dfrac{S_2}{-25} = 12.5$$

The image and the object are

$$d = 12.5-(-25) = 37.5cm$$

apart.

Answer. a) M = 2, b) d = 37.5 cm.