AP Physics 2 Exam Question:

A converging lens with a focal length of 20 cm is used to form an image of an object. The object is placed 30 cm from the lens. Determine the characteristics and location of the image formed by the lens.

Answer:

To determine the characteristics and location of the image formed by the lens, we can use the lens formula and magnification formula.

Given:

• Focal length, f = 20 cm (positive for converging lens)
• Object distance, p = 30 cm (positive for object in front of the lens)

Using the lens formula, 1/f = 1/p + 1/q, where q is the image distance, we can solve for q:

1/f = 1/p + 1/q
1/20 = 1/30 + 1/q
1/q = 1/20 - 1/30
1/q = (3 - 2)/60
1/q = 1/60
q = 60 cm

Therefore, the image distance, q, is 60 cm.

Now, let's find the magnification, M, which is given by M = -q/p:

M = -q/p
M = -(60/30)
M = -2

Therefore, the magnification, M, is -2. Since the magnification is negative, it indicates the image is inverted.

Now, we can determine the characteristics of the image formed by the lens:

1. Location of the image:

   • The image distance, q, is positive (60 cm), indicating the image is formed on the opposite side of the lens from the object.
   • The positive image distance suggests a real image is formed.

2. Nature of the image:

   • The magnification, M, is negative (-2), indicating the image is inverted.
   • The magnification value of 2 suggests that the image is magnified in size.

In summary, the converging lens with a focal length of 20 cm forms a real and inverted image, located 60 cm away from the lens. The image is also magnified by a factor of 2 in size.