question_answer

(a) Draw a ray diagram to show the formation of image by a concave lens when an object is placed in front of it.

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

(c) Find the nature and power of a lens which forms a real and inverted image of magnification ?1 at a distance of 40cm from its optical centre.

Answer:

(a)

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

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

(c) As, \[m=-1;\] hence, the lens is convex

Now,     \[m=\frac{v}{u}\]

\[\therefore \]      \[v=-u\]

Thus, object is at 2F.

\[\because \]       \[v=40\,cm\] (Given)

\[\therefore \]      \[2f=40\text{ }cm\]

\[f=20\,cm\,=0.2\,m.\]

\[P=\frac{1}{f}=\frac{1}{0.2}=+5D\] (convex lens)