Question

An object of length $2cm$ is placed at distance $1.5f$ from a concave mirror where ${}^{\prime }{f}^{\prime }$ is its focal length. Find the length of the image.

• A. 6.66 cm
• B. 5 cm
• C. 2 cm
• D. -1.33 cm

Answer 1

The correct option is D -1.33 cm

$magnification=m=\frac{-v}{u}$

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

Multiplying both sides by $u$-

$\frac{u}{v}+1=\frac{u}{f}$

$\frac{-1}{m}+1=\frac{u}{f}$

$⟹m=\frac{f}{f-u}$

$⟹\frac{h_i}{h_o}=\frac{-f}{-f+2.5f}$

$⟹\frac{h_i}{2cm}=\frac{-1}{1.5}$

$⟹h_i=-1.33cm$

Negative sign in front of height of image shows that it is inverted.

Answer-(D)