Measurement of the focal length of a converging lens

When a ray box is placed on one side of a converging (convex) lens and a screen is placed on the other side, a real image of the object (ray box) can be formed on the screen. In this experiment a slit at the front of a ray box is the object. The ray box is moved and the image located on the screen. The object distance (u) and image distance (v) are measured. 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 35 cm) and then verify its value using the above formula.

Note 2: If the ray box is inside the focal point you do not get a real image. It is virtual and in front of the lens.

Procedure:

  1. Type in a focal length for the lens
  2. Press "Apply"
  3. Using the mouse, drag the ray box to any position that produces an image
  4. Drag the base of the screen until the screen is at the sharpest image position, the intersection of the light rays.
  5. Press "Get Ruler"
  6. Measure and record the object distance and the image distance as in the table below
  7. Repeat steps 3 to 6 five more times
  8. Use the formula to calculate the focal length of the lens
  9. If you wish to repeat the experiment with a lens of different focal length just type in a new value etc.

Format of results table

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

Analysis:

The focal length of the lens 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 is as sharp as possible before taking u and v measurements
  • Avoid parallax errors (eye directly in front of metre stick) when taking measurements
  • Take all measurements from the centre of the lens