Measurement of the focal length of a concave mirror

When an object is placed in front of a concave mirror (outside the focal point), a real image is formed. The image can be seen on a screen when it is moved to the position of the image. In this experiment a slit at the front of a ray box is the object. The ray box can be moved and the screen can be moved. The object distance (u) and image distance (v) is measured each time an image is found on the screen. The focal length (f) can then be calculated using the formula: 1/f = 1/u + 1/v

Note 1: In this applet you type in a focal length (between 15 and 30 cm) and then verify its value using the above formula.

Note 2: When you move the ray box inside the focal point you do not get a real image. It is virtual and behind the mirror.

Procedure:

  1. Type in a focal length (15 to 30 cm) in the text field
  2. Press "Apply"
  3. Using the mouse, drag the ray box towards the mirror
  4. Drag the screen base to the point where the reflected rays meet to form the sharpest image
  5. Press "Get Ruler"
  6. Record the object and image distances in a table as shown below
  7. Drag the ray box to a new position, move the screen to the new image position, get the ruler and again record the distances
  8. Repeat until you have at least six sets of readings
  9. Verify that 1/u + 1/v = 1/f
  10. If you wish, repeat the experiment with a new focal length value

Analysis:

u (cm)
v (cm)
1/u
1/v
1/u + 1/v
f (cm)
           

The focal length of the mirror can be found by applying the formula to each set of u and v values as above and getting the average.

It is also possible to draw a graph, on graph paper, of 1/v (y-axis) against 1/u. The equation of the line can be compared to the standard form of linear equation, y = mx + c.

In this case it is: 1/v = -1/u + 1/f. This cuts (intercepts) the y-axis (1/v axis) when x (1/u) is zero i.e. 1/v = 0 + 1/f. Similarly the line intercepts the 1/u axis when 1/v is zero, giving us 1/u = 1/f. From your graph get the average of the two intercepts, find the reciprocal to get the value of f.

Precautions:

  • When doing this in the lab ensure that the image on the screen is as sharp as possible before measuring v
  • Avoid parallax errors (eye directly in front of metre stick) when measuring u and v
  • Measure from the centre of the back of the mirror (the point where reflection occurs) in all cases