question_answer

(a) Define focal length of a spherical lens.

(b) A divergent lens has a focal length of 30 cm. At what distance should an object of height 5 cm from the optical centre of the lens be placed so that its image is formed 15 cm away from the lens? Find the size of the image also.

(c) Draw a ray diagram to show the formation of image in the above situation.

Answer:

(a) The distance between the optical centre and focus of a spherical lens is called focal length.

(b) Given: \[f=30\text{ }cm,{{h}_{O}}=\text{ }5\,cm,\,\,\,{{h}_{I}}=?,\,\,\,v=15cm.\]

We know that,    \[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\]

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

\[\Rightarrow \]               \[u=\frac{vf}{f-v}\]

\[=\frac{-15\,\times -30}{-30+15}=-30cm\]

Now,                 \[m=\frac{v}{u}=\frac{{{h}_{I}}}{{{h}_{O}}}\]

\[\Rightarrow \]               \[{{h}_{I}}=\frac{v}{u}\,\times \mathrm{ }{{h}_{O}}=\frac{-15}{-30}\times \mathrm{ }5=2.5cm\]

(c)