To find the focal distance of the lens by different methods

Lenses, optical table, light source, distant light source

Thin lenses are of two types, converging (like the convex lenses) and diverging (like the concave lenses). Examination by eye of a double convex lens (or a plano-convex lens) will demonstrate that the lens changes the apparent size of an object, and can usually project that image onto a screen. A double concave lens (or its plano version) also alters the apparent size of an object when that object is viewed through the lens.

Parallel light will be converged by the convex lens until all of the light passes through a point on the side of the lens opposite to the entering light. On the other hand, parallel light will be spread by a diverging lens, but it will appear to the eye as coming from a point. These points are called focal points and the distance between the lens and the focal point is the focal distance, f. A good approximation to the behavior of simple lenses is that the image, s', and object, s , distances are related to the focal length as

                                                                            1/f = 1/s + 1/s'                                                                        (1)

If the image distance is positive, then the image is real and may be projected onto a screen (see figure 1 below). If the image distance is negative, then the image is virtual, but may be focused by the eye to a real image on the retina.

Figure 1. Effects of a converging lens on the light reflected from an object. The image is inverted.

Exercise 1.

Placed an object with high contrast  at a large distance from the converging lens. Practically speaking, the light from this object is parallel and will be imaged one focal length from the lens. Verify the presence of this image by projecting it on a white screen and measure the distance from the lens to the screen. Record the experimental errors.
 
 

Exercise 2.

Place a converging lens between an illuminated object and a screen. There are two positions between the object and the screen where the lens may be placed to obtain a sharp image. Measure the distance between these positions (a). Measure the distance between the object and the screen (b).  Record the experimental errors. The focal length of the lens can be found as
                                                                        f = (b² - a²)/4b                                                                (2)

Exercise 3.
Vary the source distance and measure the corresponding image distance for at least 5 data sets. Record the experimental errors. The source and the image should fit on the 1m optical table.

Exercise 1.
Record the focal distance and its error.

Exercise 2.
Calculate the focal distance using equation (2). What is the error?

Exercise 3.
Plot the inverse object distance as a function of the inverse image distance. Find the focal distance from the graph (using equation (1)), and its error. Compare the results of exercises 1, 2 and 3.