Question

A point object O is placed at a distance u>2f from a concave mirror of focal length 15 cm. The image object separation is 16 cm image being nearer. Now the mirror is cut into two halves by a horizontal plane through the axis. Two halves are shifted symmetrically about P in the vertical direction as shown with a gap<<f. The vertical separation between the two images formed is 16 mm. The numerical value of the gap is

• A. 3 mm
• B. 5 mm
• C. 10 mm
• D. 15 mm

Answer 1

The correct option is C 10 mm

$2hi=\frac{2\times 24x}{40}$

$\Rightarrow$ separation between images $=2x+2hi$

$\Rightarrow 2x+\frac{2\times 24x}{40}=16$

$\Rightarrow 2x\left[1+\frac{24}{40}\right]=16$

$2x=\frac{16\times 40}{64}$

$2x=10mm$

Hence,

option $\left(C\right)$ is correct answer.