Answer :
The mirror is located 30 cm from the object
Explanation:
To solve the problem, we can use the magnification equation, which states that:
[tex]M=\frac{y'}{y}=-\frac{q}{p}[/tex]
where
M is the magnification
y' is the size of the image
y is the size of the object
q is the distance of the image from the mirror
p is the distance of the object from the mirror
In this problem, we notice that the image formed by the mirror is erect and diminished: this means that this is a convex mirror, so the image is virtual, and this means that the image and the object are located on opposite sides of the mirror. Therefore,
[tex]p-q=40 cm[/tex] (distance of the image from the object is 40 cm, but since the image is virtual, q is the negative)
The size of the image is 1/3 that of the object, so
[tex]y'=\frac{1}{3}y[/tex]
Solving the equation for p, we find the distance between the object and the mirror:
[tex]\frac{y'}{y}=-\frac{p-40}{p}\\\\p=\frac{40}{1+\frac{y'}{y}}=\frac{40}{4/3}=30 cm[/tex]
So, the mirror is 30 cm from the object.
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The mirror is situated on 13.3 cm
The object distance is the distance of the object to the center line of the lens. This is denoted by the do d o. The image distance (many time confused with the focal length) the distance of the image to the middle line of the lens.
Given,
image distance=-40cm=v
Object distance=u=?
Magnification=m=3
we know
[tex]m = - \frac{v}{u}[/tex]
[tex]3= - \frac{-40}{u}[/tex]
[tex]3= \frac{40}{u}[/tex]
[tex]u = \frac{40}{3}[/tex]
u = 13.3 cm
What is the formula for image distance?
image_distance = (Object Distance × Focal Length of the Convex Mirror)/(Object Distance + Focal Length of the Convex Mirror) v = (u * F)/(u + F) This formula uses 2 Variables Variables Used Object Distance - Object Distance is the distance of the object from mirror.
Learn more about distance here https://brainly.com/question/15172156?
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