Question

An object $\left(O\right)$ is placed in front of a concave mirror at some distance as shown in the diagram above. Identify which of the following options best describes the image formed by the mirror?

• A. Virtual and magnified
• B. Real and erect
• C. Inverted and magnified
• D. Virtual and reduced
• E. Real and inverted

Answer 1

The correct option is E Real and inverted

According to sign convention , the distance of object from the pole of lens is negative ($-u$) and given that $u>R$.

Now by $\frac{1}{u}+\frac{1}{v}=\frac{2}{R}$

or $v=\frac{uR}{2u-R}$

but $u>R$ it means that $v$ will be negative (when we put the signs of $u$ and $R$ ) and $v<R$. $v$ will have a value between $R$ and $R/2$ .

Now magnification $m=-\frac{v}{u}=<-1$ (because $v<R$ and $u>R$)

it means inverted and smaller image

As $v$ is negative ,a real ,inverted and smaller image of the object will be formed between focus $\left(R/2\right)$ and $R$.