Question

To find the value of v for different values of u in case of a concave mirror and to find the focal length

Answer 1

Aim:
 To calculate the focal length of a concave mirror by U-V method

Apparatus required : 
V stand, Concave mirror, Screen ,candle, pencil and a scale

Procedure :
Place the concave mirror on V stand and candle and meter and arrange as shown in the figure.
Keep the candle at different places from the mirror (10cm to 80cm) along the axis and by moving the screen find the position where we get sharp image on screen.
Observations:

****************************************************
Object distance   Image distance         f=uv/u+v
     u                         v
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10cm
20cm
40cm
60cm
80m
***************************************************
Take the average of focal length.

Answer 2

apparatus :an optical bench with three uprights ,concave mirror, a mirror holder ,a knititng needle and a meter scale.
by using above apparatus and theory of mirror,we get

we know, mirror formula,
                        1/f = 1/u + 1/v 
     1/v = 1/f - 1/u 
f is the focal length, hence, is is constant when we use a concave mirror.
   Let we use concave mirror of focal length f = -15cm {with sign 
        when object distance from the pole of focal length u = -10cm
            1/v = 1/-15 - 1/(-10) = 1/10 - 1/15 = 5/150 = 1/30 cm
              v = 30 cm [image form right side with 30cm  distance from the pole
 when u = -15cm
          1/v = 1/-15 -1/(-15) = 0 ⇒ v = ∞  [image form in infinite 
  when u = - 20 cm
    1/v = 1/-15 + 1/20 = -5/300 = -1/60
     v = -60cm [ image form left side 60cm from the pole 
when u = -30cm
   1/v = 1/-15 + 1/30 = 1/-30 , v = -30cm [image form left side with equal distance of object ]
   hence, finally we observe the data is 
   focal length (f)              object (u)                                 image (v)
          -15cm                       -10cm                                   30cm
         - 15cm                      - 15cm                                   ∞
         -15cm                       -20cm                                    -60 cm
         -15cm                      -30cm                                    - 30cm 
   
after drawing u and v relation in graph, we get graph is hyperbolic.
    but when we draw the graph  of 1/v , 1/u we get straight line graph.
   as you see, 1/v(let y) = 1/u (let x ) + 1/f (constant ,c )
                     y = mx + c , this is general formula of straight line graph.