A biconvex lens is formed by using two thin planoconvex lenses, as shown in the figure. The refracti

Question

A biconvex lens is formed by using two thin planoconvex lenses, as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in figure. When an object is placed on the left side of lens at a distance of 30 cm from the biconvex lens, the magnification of the image will be :

Professor PC Thomas Classes · Answer

The biconvex lens is a combination of two plano-convex lenses. The focal length of the first lens is $\frac{1}{f_1} = (\mu_1 - 1)\left(\frac{1}{R_1} - \frac{1}{\infty}ight)$, and the second is $\frac{1}{f_2} = (\mu_2 - 1)\left(\frac{1}{\infty} - \frac{1}{-R_2}ight)$. Using standard values from the context to find the equivalent focal length yields $\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} \implies F = 20 	ext{ cm}$. Using the lens formula $\frac{1}{v} - \frac{1}{u} = \frac{1}{F}$ with $u = -30 	ext{ cm}$: $\frac{1}{v} - \frac{1}{-30} = \frac{1}{20} \implies \frac{1}{v} = \frac{1}{20} - \frac{1}{30} = \frac{3-2}{60} = \frac{1}{60} \implies v = 60 	ext{ cm}$. The magnification is $m = \frac{v}{u} = \frac{60}{-30} = -2$.