Question

Two identitical thin plano-convex glass lenses (refractive index 1.5 ) each having radius of curvature of 20 cm are placed with their convex surface in contact at the centre .The intervening space is filled with oil of refractive index 1.7.The focal length of the combination is

• A. -20 cm
• B. -25 cm
• C. -50 cm
• D. 50 cm

Answer 1

Answer: (C)

-50 cm

The intervening space will act as concave lens.

Thus, the net focal length of the combination of three lenses would be given as, $\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}$

Now by the lens makers' formula,

$\frac{1}{f_1}=(1.5-1)(\frac{1}{\infty }-\frac{1}{-20})=\frac{1}{40}$

$\frac{1}{f_2}=(1.7-1)(\frac{1}{-20}-\frac{1}{20})=-\frac{2.8}{40}$

$\frac{1}{f_3}=(1.5-1)(\frac{1}{20}-\frac{1}{\infty })=\frac{1}{40}$

$\therefore \frac{1}{f}=-\frac{0.8}{40}⟹f=-50cm$

Option C is correct.