Question #122566

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?


1
Expert's answer
2020-06-18T11:19:17-0400

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=ffS1M = \dfrac{f}{f-S_1}


or


M=S2S1M = -\dfrac{S_2}{S_1}

where f=20cmf = 20 cm is the focal length, S1=30cmS_1 = 30 cm is the distance from the  flower to the lens and S2S_2 .is the distance from the image to the lens. Substituting the values into the first equation, obtain:


M=203020=2M = \dfrac{20}{30-20} = 2

2. According to the first formula:


0.5=2525S1S1=25cm0.5 = \dfrac{25}{25-S_1}\\ S_1 = -25 cm

Now let's use the second formula:


0.5=S225=12.50.5= -\dfrac{S_2}{-25} = 12.5

The image and the object are


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

apart.


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


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