Question

when the distance of an object from a concave mirror is decreased from 15 cm . to 9 cm. the image gets magnified 3 times than that in first case . Calculate the focal length of the mirrior

Answer 1

f=27/4
or 6.75 cm


I m use mirror formula for this

Answer 2

Concept

A concave mirror incorporates a reflective surface that's curved inward and removed from the sunshine source. Concave mirrors reflect light inward to at least one point of interest.

Given

we are only if the gap of object decreased from $15cm$ to $9cm$ and therefore the image is magnified thrice that in first case.

Find

we have to seek out the distance.

Solution

Let us take $u=-x$ where $x=15,9$.

Here, we are going to use the magnification formula $m=\frac{f}{f-u}$.

When $x=15$ then $u=-15$, we get

$m_{1}=\frac{f}{f+15}$                                 ......(1)

When $x=9$ then $u=-9,$ we get

$m_{2}=\frac{f}{f+9}$                                ......(2)

It is providing that $m_{2}=3m_{1},$ we get

$\begin{aligned}\frac{f}{f+9}&=\frac{3f}{f+15}\\ 3f+27&=f+15\\ 2f&=-12\\ f&=-6\end$

Hence, the focal distance of mirror is $-6cm.$

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