Question

A convex lens of focal length \[10\,cm\] is placed at a distance of \[12\,cm\] from a wall. How far from the lens should an object be placed so as to form its real image on the wall?
A. \[30\,cm\]
B. \[15\,cm\]
C. \[120\,cm\]
D. \[60\,cm\]

Answer 1

Hint: Learn about lenses and the image forming mechanism in them. Use the Lens formula to find the distance of the object from the lens to form a real image at the wall.An optical lens is generally made up of two spherical surfaces. If those surfaces are bent outwards, the lens is called a biconvex lens or simply convex lens.

Formula used:
The Lens’s formula is given by,
\[\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}\]
where \[f\] is the focal length of the lens, \[u\] is the distance of the object from the lens, \[v\] is the distance of the image from the lens.

Complete step by step answer:
 Here we have given that the focal length of the convex lens is \[10\,cm\]. The image of the object will be at the wall so the image distance is the same as the distance of the wall. So, the distance of the image from the lens is \[v = 12\,cm\]. Now we know that the, Lens’s formula is given by, ,
\[\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}\]
So, putting the value of the focal length of the lens and the distance of the image from the lens we can calculate the distance of the object from the lens easily. So, putting the focal length of the lens \[f = 10\,cm\] and distance of the image from the lens \[v = 12\,cm\] we have,
\[\dfrac{1}{{10}} = \dfrac{1}{u} + \dfrac{1}{{12}}\]
\[\Rightarrow \dfrac{1}{u} = \dfrac{1}{{10}} - \dfrac{1}{{12}}\]
\[\therefore u = - 60\]
So, the distance of the object or object distance is \[60cm\]to the left of the lens.

Hence, option D is the correct answer.

Note: The negative sign implies that the object is to the left of the lens while the positive sign implies that the distance is to right of the lens. This is the general sign convention that is used in optics. Remember that the focal length of a convex lens is positive since parallel rays of light converge passing through a convex lens.