question_answer

One half of a convex lens of focal length 10 cm is covered with a black paper. Can such a lens produce an image of a complete object placed at a distance of 30 cm from the lens? Draw a ray diagram to justify your answer.

A 4 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. The distance of the object from the lens is 15 cm. Find the nature, position and size of the image.

Answer:

Yes, it can produce an image of a complete object placed at a distance of 30 cm from the lens.

Given: \[{{h}_{1}}=4\,cm,\,f=+20\,cm,\,u=-15\,cm\]

We know that,

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

\[\frac{1}{\upsilon }=\frac{1}{f}+\frac{1}{u}=\frac{1}{20}-\frac{1}{15}=\frac{3-4}{60}=\frac{-1}{60}\]

\[\therefore \]      Image distance, \[\upsilon =-\,60\,cm\].

Image will be virtual and erect.

Now,     Magnification, \[m=\frac{{{h}_{2}}}{{{h}_{1}}}=\frac{\upsilon }{u}\]

\[{{h}_{2}}=\frac{\upsilon }{u}\times {{h}_{1}}=\frac{-60}{-15}\times \mathrm{ }4=+16\,cm\]

The size of the image is 16 cm.