question_answer

(a) Define optical centre of a spherical lens.

(b) A divergent lens has a focal length of 20 cm. At what distance should an object of height 4 cm from the optical centre of the lens be placed so that its image is formed 10 cm away from the lens. Find the size of the image also.

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

Answer:

(a) Optical centre is a point on a lens through which ray of light passes undeviated, without suffering any refraction.

(b) Given: \[f=\text{ }20\text{ }cm,\text{ }{{h}_{0}}=4\,cm,\text{ }v=\,\,10\,cm\]

We know that,

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

\[\frac{1}{-20}=-\frac{1}{10}-\frac{1}{u}\]

\[\frac{1}{u}=-\frac{1}{10}+\frac{1}{20}\]

\[\frac{1}{u}=-\frac{-2+1}{20}=\frac{-1}{20}\]

\[u=-20cm\]

Now,     \[m=\frac{hi}{ho}=\frac{v}{u}\]

\[\frac{hi}{4}=\frac{-10}{-20}\]

\[2{{h}_{i}}=4\]

\[\Rightarrow \]               \[{{h}_{i}}=2\mathrm{cm}\]