question_answer

(a) Draw a ray diagram to show the formation of image by a convex lens when an object is placed in front of the lens between its optical centre and principal focus.

(b) In the above ray diagram mark the object-distance (u) and the image-distance (v) with their proper signs (+ve or ?ve as per the new Cartesian sign convention) and state how these distances are related to the focal length (f) of the convex lens in this case.

(c) Find the power of a convex lens which forms a real, and inverted image of magnification ?1 of an object placed at a distance of 20 cm from its optical centre.

Answer:

(a)

(b) The object distance and image distance are marked in the diagram of part (a).

The relation between v, u and f is given by the formula,

\[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\]

(c) Given, \[m=-1;\,u=-20\,cm;\,v=?,\,f=?\]

We know that, \[m=\frac{v}{u}\]

\[-1=\frac{v}{-20}\]

\[v=+\,20\,cm\]

Thus object is at 2F.

i.e.,       \[2f=20\text{ }cm\]

\[f=\frac{20}{2}=10cm=0.1m\]

\[P=\frac{1}{f}=\frac{1}{0.1}=+10D\]

The power of convex lens is +10 D.