360 PROBLEMS 



the objective is M = L//2, where L is the approximate length of the draw tube, and 

 /1 and fi are respectively the equivalent focal lengths of the eyepiece and objective. 

 Show that the combined magnifying power is 25L//1/2. 



VIII-3. It is desired to have a microscope attain a magnifying power of 1000 

 diameters. The eyepiece has an equivalent focal length of 1.5 cm and the objective 

 0.33 cm. What draw-tube length must be used? 



Ans. 20 cm. 



VIII-4. How small an object would you expect to distinguish visually when 

 using a 32-mm objective of 0.10 N.A.? How small an object can be resolved with 

 a 16-mm achromat of 0.25 N.A.? 



VIII-5. An electron is given a kinetic energy of 4 X 10 5 electron volts. What 

 is its equivalent de Broglie wavelength in centimeters? 



VIII-6. Calculate the wavelength associated with an electron moving with a 

 speed comparable to 100,000 election volts. Take into consideration the increase in 

 mass of the electron due to the theory of relativity. 



Ans. 0.03 A. 



VIII-7. The unit of magnetic field intensity is called the oersted, formerly called 

 the gauss. The oersted is defined as the intensity at a given point in a magnetic 

 field at which the field would act with the force of 1 dyne upon unit pole placed 

 there; 1 oersted = 1 dyne/1 pole. In a transverse field of 150 oersteds a cathode 

 beam traces a curve of 6-cm radius. What is the velocity of the electrons? e = 1.60 

 X 10- 20 emu. 



VIII-8. What magnetic field intensity must be applied perpendicular to a beam 

 of electrons having a velocity of 1.88 X 10 9 cm/sec so that they will be bent into a 

 circle of radius 4.25 cm? 



VIII-9. The numerical aperture of an election microscope is 0.02. Using 

 50,000 as the accelerating voltage what resolution may be obtained? 



Ans. 2.7 X 10~ 8 cm. 



VIII-10. What electron speed must be used to give an electron microscope with 



o 



magnetic coil lens a resolution of 2.0 A? 



Ans. 90 kv. 



