Question

Two identical double convex lenses each of focal length f are made of glass $\mu =\frac{3}{2}.$ If R is the radius of curvature of each of the four faces, then

• A. The focal length of the combination is half the radius of curvature of any of the four surfaces.
• B. None of these.
• C. The focal length of the combination increases if the lenses are separated by a distance f and the new focal length is twice the focal length when the lenses are in contact.
• D. The focal length of the combination decreases when they are separated by a distance f and the new focal length is half the focal length when the lenses are in contact.

Answer 1

Answer: (A), (C)

$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}+\frac{1}{R_2})$

$=(\frac{3}{2}-1)(\frac{1}{R}+\frac{1}{R})=\frac{1}{R}$

$\therefore f=R$

Combined focal length when in contact

$\frac{1}{F}=\frac{1}{f}+\frac{1}{f}=\frac{2}{f}=\frac{2}{R}$

$\therefore F=\frac{R}{2}$

Combined focal length when they are separated by $f$,

$\frac{1}{F^{\prime }}=\frac{1}{f}+\frac{1}{f}-\frac{f}{f^2}$

$\frac{1}{F^{\prime }}=\frac{1}{f}$

$F^{\prime }=f=R$

$\therefore F^{\prime }=2F$