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Q. A double convex lens made of glass of refractive index $1.56$ has both radii of curvature of magnitude $20 \,cm$. If an object is placed at a distance of $10 \,cm$ from this lens, the position of the image formed is

Ray Optics and Optical Instruments

Solution:

Here, $R_1 = 20 \,cm, R_2 = - 20 \,cm, u = -10\, cm$
and $\mu = 1.56$
Using lens make'rs formula,
$\frac{1}{f} = \left(1.56 -1\right)\left(\frac{1}{20}+\frac{1}{20}\right)$
$ \Rightarrow f = \frac{20}{0.56\times2} = 17.86 \,cm $
Now, from lens equation,
$v = \frac{uf}{u+f} = \frac{-10\times 17.86}{-10+17.86} = -22.86 \,cm$
Since $v$ is negative, the image will be formed on the same side as that of object.