Tuesday, January 20, 2015

Microscope

A microscope is a device used to see small object much magnified at the least distance of distinct vision.

Least distance of distinct vision : The minimum distance from the eye at which the objects are clearly visible is called the least distance of distinct vision. It is denoted by D. For a normal eye it is about 25 cm.

The two types of microscopes are discussed below :
1. Simple microscope or magnifying glass,
2. Compound microscope

1. Simple microscope or Magnifying glass
The size of an object depends upon the angle subtended by the object at the eye. The angle subtended depends upon the dimensions of the object and its distance from the eye. If the object is  brought nearer, the angle subtended at the eye increases and the object appears bigger and more distinct. Thus to see san object distinctly, it should be moved very near to the eye. But if it is brought near the eye at a distance less than the least distance of distinct vision, it becomes indistinct. Thus to see the object distinctly, It should be moved very close to the eye but its image should be formed at the least distance of distinct vision.

An ordinary convex lens of small focal length kept close to the eye can be used as a simple microscope or magnifying glass.

Watch makers use a single convex lens to get a magnified view of the fine parts of the watch.

Magnifying Power : The magnifying power of a simple microscope is the ratio of the angle subtended at the eye by the image as seen through the lens to the angle subtended by the object at the unaided eye, when both are placed at the least distance of distinct vision, it is denoted by M.

The mathematical formula for Magnifying Power, M is

                                            M = D/u
            
                                               = 1+D/f

Where, D is the least distance of distinct vision and is equal to v.
D being constant, the magnifying power depends upon the focal length of the lens.
       Smaller the focal length, greater will be the magnifying power of the lens.

2. Compound microscope : The magnification produced by simple microscope is small and can only be increased by decreasing the focal length of the lens. But there is a practical limit to it. Large magnification can be obtained by using compound microscope in which magnification is obtained in two stages by using two convex lenses.

Magnifying Power : Magnifying power of the microscope is defined as the ratio of the angle subtended by the image at the eye as seen through the microscope to the angle subtended by object at the unaided eye when both are placed at the least distance of distinct vision.

The mathematical formula for Magnifying Power, M is       

fe = focal length of the eye-piece
Fo = focal length of the objective

v = L = length of the microscope tube,
and u = Fo

Hence,                  M = v/u (1+D/fe)

                                 = L/Fo(1+ D/fe)

The above relation shows that magnifying power is inversely proportional to the focal length of the objective and the focal length of the eye-piece. Therefore, magnifying power can be increased by
1. taking the objective of short focal length
2. taking the eye-piece of short focal length.


Practice Problems :
1. A simple magnifier (convex lens) has a focal length of 10 cm. Find its magnifying power.
Solution :
                  f = 10 cm
Magnifying power of a simple microscope(convex lens) M = 1+D/f 
              
⇒                M = 1+25/10     
                        = 1 + 2.5    
                        = 3.5                         { D = 25 cm for normal eye}

Magnifying power of simple convex lens of f = 10 cm is 3.5

2. A simple microscope is made of a combination of two lenses in contact of powers +15D and +5D. Calculate the magnifying power of the microscope, if the image is formed at 0.25m, the least distance of distinct vision.
Solution :   
               Powers of the two lenses are
                p1 = + 15 D
and           p2 = + 5D 
                D  = distance of distinct vision = 0.25 m
∴ Power of the combination, P = + 15 + (+5)
                                            = + 20 D 
∴ Focal length of the lens, f = 1/(+20)
                                        = 0.05 m
Now, magnifying power of simple microscope,

                                  M = (1+ D/f)
                                      = 1 + 0.25/0.05
                                      = 1 + 5 = 6 (Ans.)

Some practice problems :

1. An object is placed at a distance of 15 cm from a convex lens of focal length 30 cm. The size of image formed, in comparison to size of object is
(a) same                                   (b) double
(c) half                                      (d) 4 times

2. A simple magnifier(convex lens) has  a focal length of 10 cm. Its magnifying  power is :
(a) 0.1                                       (b) 2.5
(c) 3.5                                       (d) 10

3. Distance of distinct vision for a normal eye is :
(a) 5 cm                                     (b) 25 cm
(c) 50 cm                                   (d) infinity

4. In a simple microscope, the object is placed 
(a) between F and its lens            (b) at F
(c) between f and 2f                    (d) beyond 2f

5. Which of the following is not true ?
(a) Microscope is used to see small objects.
(b) Telescope  is used to see distant objects.
(c) In a microscope objective is larger than eye piece.
(d) In a telescope objective is larger than eye piece.

6. For a simple microscope if the final image is located at the least distinct vision D from the eye placed close to the lens, the magnifying power is :
(a) D/f                                   (b) 1 + D/f
(c) f/D                                   (d) f × D

7. Ratio of focal length of the objective to the focal length of the eye piece is greater than one for :
(a) telescope                                      (b) microscope
(c) both telescope and microscope       (d) neither telescope nor microscope

8. The final image produced by a simple microscope is :
(a) virtual and erect                           (b) virtual and inverted
(c) real and erect                               (d) real and inverted

9. A convex lens acts as a simple microscope when the object is placed
(a) between F and 2F                        (b) between optical centre and focus
(c) at 2F                                           (d) at F

10. The linear magnification of an image is m. The magnification for area will be
(a) m                                              (b) m/2
(c) m2                                                                  (d) m1/2
  

11. As an object is moved from infinity towards the pole of a convex lens, the magnification of image will
(a) remain same                              (b) decrease 
(c) increase                                     (d) depend upon the presence of medium

12. Which of the following formula do not represent magnification by a lens– (where terms has usual meaning).
(a) I/O                                           (b) v/u
(c) (f – v)/f                                     (d) f/u

13. When the length of the tube of a compound microscope is increased, its magnifying power will
(a) increase                                  (b) decrease
(c) remain unchanged                    (d)become infinity

14. The magnifying power of a compound microscope in terms of magnification mo due to objective and magnifying power me by the eye piece is given by
(a) mo/me                                     (b) m× me
(c) mo+me                                    (d) me/mo

15.If the least distance of distinct vision is 25 cm, then the convex lens of focal length 5 cm acts as a magnifier of magnifying power,
(a) 5                                          (b) less than 5
(c) 6                                          (d) more than 6


Answers :
1. b
2. c
3. b
4. a 
5. c
6. b
7. a
8. a
9. b
10. c
11. c
12. d
13. b
14. b
15. c


Note:
1. When the image formed is virtual substitute v = – D in the lens formula.
    Where     u  =  object distance
    and         v  =  image distance


Courtesy:R.A.Banwat

6 comments: