Question

Two thin similar convex glass pieces are joined together front to front with its rear portion silvered such that a sharp image is formed $20cm$ from the mirror. When the air between the glass pieces is replaced by water $\left(m_w=4/3\right)$, then the image formed from the mirror is at a distance of

• A. 8 cm
• B. 10 cm
• C. 6 cm
• D. 12 cm

Answer 1

Answer: (D)

Initially it is simply a concave mirror with $f=-20cm,R=40cm$
$\therefore$ Power of mirror $\left(P_m\right)=\frac{1}{8}$
$=\frac{1}{0.2}=5D$
Focal length of lens $=\frac{R}{2(\mu -1)}$
$=\frac{40}{2\times \left(\frac{4}{3}-1\right)}$
$=60cm$
Power of lens $=\frac{1}{0.5}$
$=\frac{100}{50}D$
$\therefore$ Equivalent power $=2P_L+P_m$
$P=\frac{50}{6}$
Net focal length $=\frac{1}{P}$
$=\frac{6}{50}\times 100$
$=12cm$