A beam of light converges towards a point O, behind a convex mirror of focal length 20cm.
Q. Find the magnification and nature of the image when point O is 10cm behind the mirror. a. $2$(virtual,inverted) b. $3$(real, inverted) c. $5$(virtual, enlarged) d. $2$ (real, erect)

a. For this situation, the object will be virtual as shown in the figure. Given: $u=+10cm$ and $f=+20cm$ To find: The position and characteristics of the image Solution: Using the mirror formula, $\frac{1}{v}+\frac{1}{+10}=\frac{1}{+20}$ Simplifying, $v=-20cm$ Therefore, the image will be at a distance of 20cm in front of the mirror and will be real, erect, and enlarged with $m=-\left(20/10\right)=+2$. b. For this situation also, the object will be virtual as shown in the figure. Given: $u=+30cm$ and $f=+20cm$ To find: The position and characteristics of the image Solution: Using the mirror formula, $\frac{1}{v}+\frac{1}{+30}=\frac{1}{+20}$ Simplifying, $v=+60cm$ Therefore, the image will be at a distance of 60cm behind the mirror and will be virtual, inverted, and enlarged with $m=-\left(+60/30\right)=-2$.