Question

An object was placed $25$ cm in front of a converging lens with a focal length of $20$ cm . A concave mirror with a focal length of $15$ cm was placed $120$ cm behind the lens. Which of these describes the final image ?

• A. Real , large
• B. Virtual, erect
• C. Real, inverted
• D. Virtual, inverted

Answer 1

The correct option is A Real , large

*First image is formed by the lens which is real and then it serves as a real object for mirror and inturn if it forms a real image it again serves as a real object for the lens and finally he image formed by the lens due to this image object is the final image*
image formed by lens be at $v_1$ ,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}=\frac{1}{20}-\frac{1}{25}$
$v_1=100$
$120-100=20$ will be distance of object for mirror
let v2 be image distance
$\frac{1}{v_2}-\frac{1}{20}=-\frac{1}{15}$
$\frac{1}{v_2}=-\frac{1}{15}+\frac{1}{20}$
$v_2=60$
$120-60=60$ will be new distance of real object for lens
v be final image distance
$\frac{1}{v}+\frac{1}{60}=\frac{1}{20}$
$\frac{1}{v}=\frac{1}{20}-\frac{1}{60}$
$v=30cm.$

final image is REAL
magnification = $\frac{v_1}{u}\times \frac{-v_2}{v_1}\times \frac{v}{v_2}$
$=-4\times -3\times 0.5$
$=6$
final image is LARGE
option A is correct