Question

A mirror forms an erect image 40cm from the object and one third its height where must the mirror be situated ​

Answer 1

The mirror is located 30 cm from the object

Explanation:

To solve the problem, we can use the magnification equation, which states that:

$M=\frac{y'}{y}=-\frac{q}{p}$

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,

$p-q=40 cm$ (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

$y'=\frac{1}{3}y$

Solving the equation for p, we find the distance between the object and the mirror:

$\frac{y'}{y}=-\frac{p-40}{p}\\\\p=\frac{40}{1+\frac{y'}{y}}=\frac{40}{4/3}=30 cm$

So, the mirror is 30 cm from the object.

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Answer 2

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

$m = - \frac{v}{u}$

$3= - \frac{-40}{u}$

$3= \frac{40}{u}$

$u = \frac{40}{3}$

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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