Question

Look at the ray diagram shown, what will be the focal length of the $1^{st}$ and $2^{nd}$ lens, if the incident light ray passes without any deviation?

• A. $-5$cm and $+10$cm
• B. $+5$cm and $+10$cm
• C. $-5$cm and $+5$cm
• D. $+5$cm and $-5$cm

Answer 1

The correct option is D $+5$cm and $-5$cm

For lens 1 the object is at infinity thus $u=\infty$, hence its image will form at focal length,and as per the figure provided image distance $v=5cm$ and is real, inverted and diminished ,thus the focal length of lens 1 $f_1=+5cm$.

Now for lens 2 image so formed by lens 1 will be the object for lens 2 which is at a distance of 5 cm away from the lens 2.

Assuming that the image will be formed at infinity we can conclude that the object for lens 2 is at focal length of lens 2, thus focal length of lens 2 $f_2=-5cm$ negative sign provided as the object lies in front of the lens and as mentioned earlier $f=u$ when $v$ is formed at infinity.