The Concave mirror - u-v method

Materials Required

  • Concave mirror
  • Stand
  • Screen
  • Illuminated wire gauze.
  • Metre scale

Real lab Procedure

By distant object method :

  • Fix the given concave mirror on the stand and place it on a table, facing towards a distant object.
  • Arrange the screen on the table so that the image of the distant object is obtained on it.
  • Measure the distance between mirror and screen using a metre scale. It can be taken as the focal length (f) of the mirror.

By u-v method : 

  • Using the focal length obtained by distant object method set the values of u (distance between mirror and object) ranging from 1.5f to 2.5f. Divide the range into a number of equal steps.
  • Place the mirror in front of an illuminated wire gauze. It acts as the object.
  • Now, fix the mirror at the distance u (which is obtained as 1.5f) from the wire gauze.
  • Place the screen on the table facing the mirror in such a way that the reflected image lies on the screen.
  • We can adjust the position of the screen to get the clear image of the wire gauze.
  • Keeping the distance between object and mirror fixed, adjust the position of screen in order to get the clear image of the object.
  • Measure the distance between mirror and wire gauze, as well as mirror and screen. Take these values as u and v respectively.
  • Record the values of u and v in a tabular column.
  • Calculate the focal length of the given concave mirror by using the relation, f = uv/(u+v).
  • Repeat the experiment for different values of u (up to 2.5f) and in each time, measure v and record it in the tabular column.
  • Calculate the focal length (f) of the concave mirror each time.
  • Calculate the mean of all focal lengths to get the correct focal length of the given concave mirror.
  • The focal length of the mirror can also be measured graphically by plotting graphs between u & v, and 1/u & 1/v.
  • We can repeat the experiment with concave mirrors of different focal lengths.

Simulator Procedure (as performed through the Online Labs)

  • Select the focal length using the slider.
  • Click on the ‘Light On/Off’ button to turn On/Off the wire gauze.
  • Select the distance between the mirror and the object (u) using the slider.
  • Change the distance between the mirror and the screen (v) suing the slider to get a clear image of the wire gauze on the screen.
  • You can calculate the focal length of the mirror using the equation,

                                           f=\frac{uv}{u+v}

  • You can verify your result by clicking on the ‘Show result’ button.
  • To redo the experiment, click the ‘Reset’ button.

Observations

No.

Distance between the mirror and

1/u

(cm-1)

1/v

(cm-1)

\small f =\frac{uv}{u+v} 

(cm)

Object, u

(cm)

Image, v

(cm)

1        
2        
3        
4        
5        

                                                                                                                Mean, f = ………. cm

                                                                                                                           = ………. ×10-2 m

Calculations:

Calculate the value of focal length (f) each time and find its mean.

Plot a graph with u along X axis and v along Y axis by taking same scale for drawing the X and Y axes. Draw the bisector OA and join OC and OB. Thus, OC=OB= 2f. Calculate the focal length from this.

Plot a graph with 1/u along X axis and 1/v along Y axis by taking same scale for drawing the X and Y axes. The graph is a straight line intercepting the axes at A and B. Then OA=OB= 1/f. Calculate the focal length from this.

              

                       u -v Graph                                                          1/u - 1/v Graph  

From u-v graph,

                        OB =….....….cm

                        OC = ...……..cm

                         \small f=\frac{OB+OC}{4}

                             =  ........... cm

From 1/u – 1/v graph,

                       OA =…………cm

                       OB =…...…... cm

                        \small f=\frac{2}{OA+OB}

                            = ............ cm

 

Results

The focal length of the given concave mirror, f 

                                              By u-v method          = ……..×10-2 m

                                              From u-v graph         = .……..×10-2 m

                                              From 1/u- 1/v graph   = ……...×10-2 m

 

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