Question

Derive an expression for magnifying power of refrecting type telescope

Answer 1



Ray diagram of simple microscope


In the figure, an object AB is placed between C and F such that a magnified erect image A’B’ is formed. If the observer’s eye is close to the lens; then the distance CB’ is equal to the least distance of distinct vision. Magnifying power (m) of a simple microscope is the ratio of the angles subtended by the image and the object on the eye, when both are at the least distance of distinct vision from the eye. If the angle subtended by the object and the image on the eye is and , respectively, then according to definition of magnifying power 

From the diagram, ...(i)
And ...(ii)
Dividing equation (ii) by (i), we get

For small angle, 
Therefore, 
Suppose CB = –u, distance of the object from the lens
CB’ = –v, distance of the image from the lens
Then, ...(iii)
Now, using lens formula

or 
or ...(iv)
Now, magnifying power of the microscope