A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $f$ , as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

• A

  
• B

  
• C

  
• Correct answer
  D

  

Solution

Distance of point A is $\frac{f}{2}$
Let A' is the image of A from mirror, for this image
$\frac{1}{v}+\frac{1}{-\frac{f}{2}}=\frac{1}{-f}$
$\frac{1}{v}=\frac{2}{f}=\frac{1}{f}=\frac{1}{f}$
Image of line AB should be perpendicular to the principle axis and image of F will form at infinity, therefor correct image diagram is


$\frac{f}{f-u}=\frac{h_2}{h_1}$
$h_2=\frac{-f\left(f-x\right)}{-f+x}$
$h_2=f$

Hence, the correct answer is option: 'D'.