Problem 7

Determination of the focal length of a negative lens: In class you will be given a negative lens in order to determine its focal length. Can you do this by combining or using a positive lens of any focal length? Explain clearly with ray diagrams. If the two lenses are separated by a distance d then the back focal length measured from the closest surface of the second lens is given by.

To use this result you need to have the object at a distance more than 10f² (f is the focal length of the positive lens) or use a collimated laser beam. In this formula either f₁ or f₂ could be the focal length of the diverging lens. If the first lens is the positive lens then the separation distance d must be less than f₁=f_p (i.e., d<f_p) regardless the power of the lenses. If the first lens is the negative lens then the separation distance d must be larger than f₁+f₂  (i.e., d>f_p+f_N) for |f_N|<f_p. If the first lens is the negative lens and |f_N|>f_p then the separation distance d  can take any value.

A simple and accurate way of determining the focal length of a negative lens can be done using the thin lens formula. Although this can be done with any positive lens it is more appropriate to use a strong one . Fix the distance between the positive lens and the object (make sure that this distance is larger than the focal length. Why?). Find the image of the object on a screen and record the image distance. Now insert the negative lens between the screen and the positive lens as close as possible to the screen. Move the screen until you find the image and record the image distance relative to the center of the negative lens. Now you can use the lens formula to find the focal length of the negative lens. Notice that object distance relative to the negative lens is the image distance formed by positive lens minus the separation between the lenses.