Question

A plano-convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now this lens has to be formed to form the image of an object. Find the distance from this lens, an object is to be placed in order to have a real image of the size of the object

Answer 1

A kind of convex lens which is used for directing parallel rays of light to a single point, Plano-Convex lenses are the best option. They can be used for concentrating, gathering and collimating the light.

Complete step by step answer:
Refractive index of the lens, $\mu = 1.5$
Radius of curvature, $R = 30cm$
If the curved surface of a plano-convex is silvered, the focal length(F) of the lens is given by,
\left( {\dfrac{1}{F}} \right) = \left( {\dfrac{{2\mu }}{R}} \right) \\\
$\implies F= \left( {\dfrac{R}{{2\mu }}} \right)$
$\implies F= \left( {\dfrac{{30}}{{2 \times 1.5}}} \right)$
$\implies F= \dfrac{{30}}{3}$
\implies F= 10cm \\\

The real image of the object will be equal to the size of the object and the object distance u is given by,
$u = 2F$
$\implies u= 2\times 10$
$\implies u= 20cm$

Additional Information:
Generally, plano-convex lenses are used for directing high power laser pulses towards the target. With reduced distortion, beam focusing is carried out using plano-convex lenses. These lenses are cheap compared to bi-convex lenses.

Note:
In real time applications, Plano-convex lenses are the most widely used ones, where the object being imaged is far away from the lens and this is called infinite conjugate in optical terms and an example of this condition is the focusing of light from a distant object such as a star.