Respuesta :
Answer:
The image is produced 60 cm behind the mirror
The focal length of the mirror is 30 cm
Explanation:
u = Object distance = 20 cm
v = Image distance
f = Focal length
m = Magnification = 3
[tex]m=-\frac{v}{u}\\\Rightarrow 3=-\frac{v}{20}\\\Rightarrow v=-3\times 20\\\Rightarrow v=-60\ cm[/tex]
The image is produced 60 cm behind the mirror
[tex]\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\\\Rightarrow \frac{1}{f}=\frac{1}{20}+\frac{1}{-60}\\\Rightarrow \frac{1}{f}=\frac{1}{30}\\\Rightarrow f=\frac{30}{1}=30\ cm[/tex]
The focal length of the mirror is 30 cm
The distance of the image is 60 cm and the focal length of this concave mirror is 30 cm.
What is focal length of the lens?
The focal length of the lens is length of the distance between the middle of the lens to the focal point.
It can be find out using the following formula as,
[tex]\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}[/tex]
Here, (v)is the distance of the image, (u) is the distance of the object, and (f) is the focal length of the lens.
Here, the concave mirror produces a real image that is three times as large as the object. The object is 20 cm in front of the mirror, and the concave mirror produces a real image that is three times as large as the object.
Hence, the value of magnification of the mirror is 3.
The object distance is 20 cm thus the image distance, using the magnification formula, can be given as,
[tex]m=\dfrac{v}{u}\\3=\dfrac{v}{20}\\v=60\rm cm[/tex]
Put the values in the lens formula as,
[tex]\dfrac{1}{60}+\dfrac{1}{20}=\dfrac{1}{f}\\f=30 \rm \; cm[/tex]
Hence, the distance of the image is 60 cm and the focal length of this concave mirror is 30 cm.
Learn more about the focal length here;
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