question_answer

Four double convex lenses, with the following specifications are available:  

Lens	Focal length	Aperture
A	100 cm	10 cm
B	100 cm	5 cm
C	10 cm	2 cm
D	5 cm	2 cm

  Which two of the given four lenses, should be selected as the objective and eyepiece to construct an astronomical telescope and why? What will be the magnifying power and normal length of the telescope tube so constructed? Write the advantages of reflecting type telescope over such a telescope. Or Which two of the above four lenses should be selected as objective and eyepiece of a compound microscope and why? How can the magnifying power of such a microscope be increased? Draw a labelled ray diagram for the image formation in such a microscope.                 

Answer:

                For constructing astronomical telescope, lens A should be used as objective because of its large focal length and large aperture. Lens D should be used as its eyepiece because of its small focal length and small aperture. \[m=\frac{{{f}_{0}}}{{{f}_{e}}}=\frac{100}{5}=20\] Normal length \[=\text{ 1}00\text{ }+\text{ 5 }=\text{ 1}0\text{5 cm}\]Advantages of reflecting telescope are: (i) No chromatic aberration. (ii) Bright image because there is no loss of intensity due to reflection and absorption by objective. Or For constructing compound microscope, the lens D should be used as objective and C as the eyepiece because the lenses should have small focal length and the focal length of the objective should be smaller then that of the eyepiece. Here      \[m=-\frac{{{\upsilon }_{0}}}{{{f}_{0}}}\left( 1+\frac{D}{{{f}_{e}}} \right)\] The magnifying power of a compound microscope can be increased by taking both \[{{f}_{0}}\] and \[{{f}_{e}}\] small. For the ray diagram showing the formation of image in a compound microscope, see Fig.