Question

Two identical double convex lenses each of the focal length $f$ are made of glass of $\mu =1.5$. If $R$ is the radius of curvature of each of the four faces. Then :
(1) the focal length of combination is half the radius of curvature of any of the four faces
(2) the focal length of combination increases if the lenses are separated by a distance $f$ and the new focal length is twice its focal length when the lenses are in contact
(3) the focal length of combination decreases when the lenses are separated by a distance $f$ and the new focal length is half its focal length when the lenses are in contact
(4) none of the above

• A. 1 and 2 are correct
• B. 2 and 3 are correct
• C. 1 and 4 are correct
• D. 1,2 and 4 are correct

Answer 1

Answer: (A)

$\frac{1}{f}=(\mu -1)\left(\frac{1}{R_1}+\frac{1}{R_2}\right)$
Or $\frac{1}{f}=\frac{1}{2}\times \frac{2}{R}$
Or $R=f$
$\therefore \frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{f}+\frac{1}{f}=\frac{2}{f}$
$\therefore F=\left(\frac{F}{2}\right)$
$\therefore$ Focal length of the combination
$\frac{f}{2}=\frac{R}{2}=$ half the radius of curvature.