Question

The radii of curvature of convex - concave lens are 0.04 m and 0.05 m respectively. If its R.I. is 1.5. The focal length of the lens is

Answer 1

Hint: we are given radius of curvature of convexo-concave lens. Convex lens is a converging lens and its focal length is positive. Concave lens is a diverging lens and its focal length is negative. Given the refraCtive index, we can use the lens maker formula here.

Complete step by step answer:
The lens maker formula is given by \[\dfrac {1}{f}=(\mu -1)\{\dfrac {1}{{{R}_{1}}}-\dfrac {1}{{{R}_{2}}}\}\]
Here f is the focal length of the combined entity, \[\mu \]is the refractive index of the material out of which the lens has been carved. \[{{R}_{1}}\]is the radius of curvature of sphere 1 and \[{{R}_{2}}\]is the radius of curvature of sphere 2
Here, the focal length of concave side is -0.04 m and for convex side it is 0.05m
Substituting in the lens maker formula,
$
\dfrac {1}{f}=(1.5-1)\{\dfrac {-1}{0.04}+\dfrac {1}{0.05}\} \\
\implies \dfrac {1}{f}=\dfrac {-0.01}{0.04\times 0.05}\times 0.5 \\
\implies f=-0.4m \\
$

So, the focal length of the lens is -0.4 m.

Additional information- Power of a lens is defined as the reciprocal of the focal length in (m). It is measured in diaptore. Convex lens power is positive while for the concave lens it is negative. Power means the ability of the lens to bend to make a sharp image on the retina.

Note:
While doing problems in optics, we have to keep in mind the sign convention. For convex lenses take the focal length as positive and for concave lenses take the focal length as negative. Convex lens converges parallel rays of light while a concave lens diverges parallel rays of light.