Question

An object is placed at a distance of \[10cm\] from a convex lens of a focal length of $15cm$. Find the position and nature of the image.

Answer 1

Hint: For a convex mirror, the focal length is taken as positive as the centre of curvature and focus always lie behind the convex mirror. The object distance is taken as negative as it is always Infront of the mirror. We can use the mirror formula for the above question to find out the image and the properties of the image.
Formula used:
$\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}$

Complete step-by-step solution:
Let us assume the distance of the image from the centre of convex mirror as $v$. Given the object distance and the focal length of the convex mirror as $10cm,15cm$respectively.
Applying these values to the mirror formula, we get,
$\begin{align}
  & \dfrac{1}{15}=\dfrac{1}{v}+\dfrac{1}{-10} \\
 & v=6cm \\
\end{align}$
Therefore, the image is formed at a distance of $6cm$from the centre of the convex mirror. As the distance of the image is positive, the image is formed behind the mirror or to the right of the mirror and the image is virtual and erect.

Additional information: Convex mirror is a curved mirror where the surface bulges outside or towards the light source. This bulging out surface reflects light outwards and is not used to focus light. The image is normally smaller than the object from the distance but gets larger as the object gets closer to the convex mirror. The convex mirror is also called a diverging mirror. These mirrors are used inside the building, making sunglasses, magnifying glass, in security and telescopes too.

Note: We usually get confused between the convex mirror and convex lens, which are quite opposite. The convex mirror will diverge light rays and the convex lens will converge the light rays. The same goes with the concave lens and mirror. Concave lens will converge and concave lens will diverge light rays.Sign convention for solving these type problems is must for calculations.