Question

The effective focal length of the lens combination shown in the figure in - 60 cm. The radii of curvature of the curved surfaces of the Plano-convex lenses are 12 cm each and refractive index of the material of the lens is 1.5. The refractive index of the liquid is:

• A. 1.33
• B. 1.42
• C. 1.53
• D. 1.60

Answer 1

Answer: (D)

The system is equivalent to combination of three lenses in contact, i.e.,
$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}$ But by lens Makers formula $\frac{1}{f_1}=(1.5-1)\left(\frac{1}{-\infty }-\frac{1}{-12}\right)=0.5\times \frac{1}{12}=\frac{1}{24}$ $\frac{1}{f_2}=(\mu -1)\left(\frac{1}{-12}-\frac{1}{12}\right)=-\left(\frac{\mu -1}{6}\right)$ $\frac{1}{f_3}=(1.5-1)\left(\frac{1}{12}-\frac{1}{\infty }\right)=\frac{1}{24}$ Also $F=-60cm$ $\therefore$ $\frac{1}{-60}=\frac{1}{24}-\frac{(\mu -1)}{6}+\frac{1}{24}=-\frac{(\mu -1)}{6}+\frac{1}{12}$ or $\frac{(\mu -1)}{6}=\frac{1}{12}+\frac{1}{60}$ or $\frac{(\mu -1)}{6}=\frac{5+1}{60}+\frac{6}{60}$ or $(\mu -1)=\frac{36}{60}=0.6$ or $\mu =0.6+1=1.6$